The spatial phase fluctuations of the fundamental laser mode due to spontaneous emission

А. В. Белинский, Anatolii S Chirkin

A calculation is reported of the degree of spatial coherence of the fundamental radiation mode subject to phase fluctuations in space. It is shown that the degree of spatial coherence (within the beam width) is perturbed only slightly by these fluctuations, compared with subthreshold excitation of higher transverse modes.

J H Hannay, Daniel E. Field

Markus Pollnau

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.

Hermann Haken

Naveen K. Singh, Richard D’Souza, Q. V. Lawande +1 more

Marlan O. Scully, Muhammad Suhail Zubairy

As discussed in the last three chapters, the fundamental source of noise in a laser is spontaneous emission. A simple pictorial model for the origin of the laser linewidth envisions it as being due to the random phase diffusion process arising from the addition of spontaneously emitted photons with random phases to the laser field. In this chapter we show that the quantum noise leading to the laser linewidth can be suppressed below the standard, i.e., Schawlow–Townes limit by preparing the atomic systems in a coherent superposition of states as in the Hanle effect and quantum beat experiments discussed in Chapter 7. In such coherently prepared atoms the spontaneous emission is said to be correlated. Lasers operating via such a phase coherent atomic ensemble are known as correlated spontaneous emission lasers (CEL). An interesting aspect of the CEL is that it is possible to eliminate the spontaneous emission quantum noise in the relative linewidths by correlating the two spontaneous emission noise events. A number of schemes exist in which quantum noise quenching below the standard limit can be achieved. In two-mode schemes a correlation between the spontaneous emisson events in two different modes of the radiation field is established via atomic coherence so that the relative phase between them does not diffuse or fluctuate. In a Hanle laser and a quantum beat laser this is achieved by pumping the atoms coherently such that every spontaneously emitting atom contributes equally to the two modes of the radiation, leading to a reduction and even vanishing of the noise in the phase difference.