We revisit the integro-differential ‘Maxwell–Bloch’ equations that describe the dynamic properties of single-mode inhomogeneously broadened lasers, with a strong harmonic expansion analysis carried up to the third order in field amplitude. In particular, we extract a closed form expression of its long-term eigenpulsation that naturally yields an iterative algorithm to build, analytically , the regular pulsing solutions of the system. Despite the complicated nature of the equations due to the presence of an integral over the polarization, the method allows for the disclosure of quite the same instructive information as those given by the much simpler Laser–Lorenz case.
Recent advances in laser technology have led to the production of ultrashort electromagnetic pulses of very high peak power. In this paper we develop a theory which describes the transient behavior of such pulses in a laser amplifier. The effects of atomic coherence and inhomogeneous broadening, necessary for a complete treatment of the problem, are included. In the present development, the degree of homogeneous and inhomogeneous broadening is variable. The two-level active atoms are characterized by a phase memory time
T2 and an inhomogeneous frequency distribution (which leads to a reversible decay time
T2∗). The field (Maxwell) and atomic (Schr\"odinger) equations are coupled in a self-consistent manner as in Lamb's theory of an optical maser. The resulting equations are solved analytically in certain limits, while the general case is integrated numerically. The emphasis is placed on the situation in which
T2∗ and the pulse width are much shorter than
T2. Thus our main effort is devoted to the physics of the inhomogeneously broadened system. The theory itself, however, contains the effects of both forms of broadening. The basic difference between inhomogeneous and homogeneous broadening is discussed. In the former case, the decay of radiation is caused by the dephasing of dipoles, and is reversible. The atomic memory is retained during the dephasing, and an internal reflection of the atomic coordinates, as is exemplified in the "photon echo" process, will cause the dipoles to rephase. The phonon interruptions or atomic collisions that bring about the homogeneous broadening are random processes which lead to an irreversible destruction of the atomic phase memory. The implications of the reversible versus irreversible decay processes are seen to have important consequences in the problem of pulse amplification.