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Optics Express

Formation of positive feedback and coherent emission in a cavity-free system

A. A. Zyablovsky, Iliya V. Doronin, E. S. Andrianov, Alexander Pukhov, Yu. E. Lozovik, Alexey P. Vinogradov, Alexander A. Lisyansky

Published Nov 18, 2019• 6 citations
Publisher

Abstract

We develop a theory of lasing of a collection of pumped active atoms without a resonator (either regular or random). Due to spontaneous emission into free space, phases of free space electromagnetic modes fluctuate. These phase fluctuations can be reduced to frequency fluctuations. The closer the frequency of fluctuation to the transition frequency of the active atoms, the higher lifetime of the fluctuation. We show that because of this, the average frequency of modes pulls toward the transition frequency. This leads to a maximum in the density of states of the electromagnetic field and a decrease of the mode group velocity. Consequently, the coupling of modes with atoms as well as the lifetime of fluctuations increase. Thus, mode pulling provides positive feedback. When the pump rate exceeds a certain threshold, the lifetime of one of the realized fluctuations diverges, and radiation becomes coherent.

DOI
10.1364/oe.27.035376

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We develop a theory of lasing of a collection of pumped active atoms without a resonator (either regular or random). Due to spontaneous emission into free space, phases of free space electromagnetic modes fluctuate. These phase fluctuations can be reduced to frequency fluctuations. The closer the frequency of fluctuation to the transition frequency of the active atoms, the higher lifetime of the fluctuation. We show that because of this, the average frequency of modes pulls toward the transition frequency. This leads to a maximum in the density of states of the electromagnetic field and a decrease of the mode group velocity. Consequently, the coupling of modes with atoms as well as the lifetime of fluctuations increase. Thus, mode pulling provides positive feedback. When the pump rate exceeds a certain threshold, the lifetime of one of the realized fluctuations diverges, and radiation becomes coherent.
It is commonly accepted that a collection of pumped atoms without a resonator, which provides feedback, cannot lase. We show that intermodal coupling via active atoms pulls the frequencies of the free-space modes towards the transition frequency of the atoms. Although at a low pump rate mode phases randomly fluctuate, phase realizations at which interference of pulled modes is constructive emerge. This results in an increase of stimulated emission into such realizations and makes their lifetime longer. Thus, mode pulling provides positive feedback. When the pump rate exceeds a certain threshold, the lifetime of one of the realizations diverges, and radiation becomes coherent.
Usually, the cavity is considered an intrinsic part of laser design to enable coherent emission. For different types of cavities, it is assumed that the light coherence is achieved by different ways. We show that regardless of the type of cavity, the lasing condition is universal and is determined by the ratio of the width of the atomic spectrum to the product of the number of atoms and the spontaneous radiation rate in the laser structure. We demonstrate that cavity does not play a crucial role in lasing since it merely decreases the threshold by increasing the photon emission rate thanks to the Purcell effect. A threshold reduction can be achieved in a cavity-free structure by tuning the local density of states of the electromagnetic field. This paves the way for the design of laser devices based on cavity-free systems.
We consider the problem of reducing the contributions of pump and spontaneous-emission noise to the output noise of a laser field. We consider two models based on an atomic medium, one analytic, the other involving numerical simulation of a sequence of pump cycles. The predictions of both models are shown to agree. For regular pump excitation the intensity fluctuations of a laser well above threshold may be reduced to zero at the cavity resonance frequency if the ratio of the lifetimes of the upper and lower lasing levels is sufficiently large that spontaneous emission is suppressed. When the atomic lifetimes are comparable, spontaneous emission reduces the amount of noise reduction. For example, for equal atomic lifetimes regular pump excitation will result in a maximum noise reduction in the output field of one-half the shot-noise limit.
A detailed analysis of the dynamics of the cavity radiation of a coherently pumped correlated emission laser is presented. The phase fluctuation and dephasing are found to affect the time evolution of the two-mode squeezing and intensity significantly. The intensity and degree of the two-mode squeezing increase at early stages of the process with time, but this trend changes rapidly afterwards. It is also shown that they increase with phase fluctuation and dephasing in the strong driving limit; however, the situation appears to be opposite in the weak driving limit. This essentially suggests that the phase fluctuation and dephasing weaken the coherence induced by a strong driving mechanism so that the spontaneous emission gets a chance. Moreover, the degree of two-mode squeezing turns out to increase with the rate of injection of the atoms into the cavity only at early stages, whereas the mean photon number increases throughout the lasing process. The other important aspect of the phase fluctuation, in this regard, is the relaxation of the time at which the maximum squeezing is manifested as well as the time in which the radiation remains in a squeezed state.
We study the collective emission of a beam of atomic dipoles into an optical cavity. Our focus lies on the effect of a finite detuning between the atomic transition frequency and the cavity resonance frequency. By developing a theoretical description of the coupled atom-cavity dynamics we analyze the stationary atomic configurations including a superradiant phase where the atoms undergo continuous monochromatic collective emission. In addition, we derive an analytical formula for the cavity pulling coefficient which characterizes the displacement of the emission frequency towards the cavity frequency. We find that the pulling is small if the cavity linewidth is much larger than the collective linewidth of the atomic beam. This regime is desired for building stable lasers because the emission frequency is robust against cavity length fluctuations. Furthermore, we investigate the stability of the atomic phases and compare our theoretical predictions with numerical results. Remarkably, we also find polychromatic emission regimes, where the spectrum has several frequency components while the light output is still superradiant.
We review the physics underlying the process of spontaneous emission, with a special focus on spontaneous emission into a resonator mode. We define the mode volume, verify the fundamental modal dimensions, present the spectral mode profile, the coherence time, the Q-factor, the Füchtbauer-Ladenburg equation, and the Purcell factor, and discuss their influence on different types of lasers. We obtain the relation between peak emission cross section, radiative lifetime, and emission linewidth. By interpreting spontaneous emission as stimulated emission driven by vacuum fluctuations, we derive the spontaneous-emission rate into a resonator mode and establish physical expressions for the fractions of spontaneous emission and total decay from the upper laser level into this mode. Furthermore, we discuss coupling of the atomic system with the coherent field inside a lasing resonator mode, resulting in the formation of a Mollow triplet, and demonstrate that it leads to a reduction of the spontaneous-emission rate by a factor of 2.