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Optics Express

Lasing dynamics of super and sub luminal lasers

Jacob Scheuer, M. S. Shahriar

Published Dec 8, 2015• 21 citations
Publisher

Abstract

We study theoretically the lasing properties and the cavity lifetime of super and sub-luminal lasers. We find that obtaining the necessary conditions for superluminal lasing requires care and that a laser operating under these conditions can under some conditions tend towards bi-frequency lasing. In contrast, conditions for a subluminal laser are less stringent, and in most situations its steady-state properties are well predicted by the self-consistent single-frequency laser equations. We also study the relaxation time of power perturbation in super and sub-luminal lasers using a finite-difference-time-domain tool and present the impact of the lasing power, the group velocity and the dispersion properties of the cavity on the relaxation dynamic of such perturbations. For the subluminal laser, we find that the time constant changes by a factor that is close to the group index. In contrast, for the superluminal laser, we find that the time constant does not change by the factor given by the group index, and remains close to or above the value for an empty cavity. These finding may be interpreted to imply that the quantum noise limited linewidth of the subluminal laser decreases with increasing group index, while the same for the superluminal laser does not increase with decreasing group index. The implications of these findings on the sensitivity of sensors based on these lasers are discussed in details.

DOI
10.1364/oe.23.032350

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We study theoretically the lasing properties and the cavity lifetime of super and sub-luminal lasers. We find that obtaining the necessary conditions for superluminal lasing requires care and that a laser operating under these conditions can under some conditions tend towards bi-frequency lasing. In contrast, conditions for a subluminal laser are less stringent, and in most situations its steady-state properties are well predicted by the self-consistent single-frequency laser equations. We also study the relaxation time of power perturbation in super and sub-luminal lasers using a finite-difference-time-domain tool and present the impact of the lasing power, the group velocity and the dispersion properties of the cavity on the relaxation dynamic of such perturbations. For the subluminal laser, we find that the time constant changes by a factor that is close to the group index. In contrast, for the superluminal laser, we find that the time constant does not change by the factor given by the group index, and remains close to or above the value for an empty cavity. These finding may be interpreted to imply that the quantum noise limited linewidth of the subluminal laser decreases with increasing group index, while the same for the superluminal laser does not increase with decreasing group index. The implications of these findings on the sensitivity of sensors based on these lasers are discussed in details.
Superluminal lasers operate under the condition in which the average group velocity in the cavity exceeds the vacuum speed of light, or alternatively, the group index is between 0 and 1 [1]. It has been shown in previous works that the sensitivity of the lasing frequency of such a laser with respect to a change in its optical roundtrip due to an external perturbation is expected to be substantially larger than that of a conventional laser, with an enhancement factor which is inversely proportional the group index [2]. This property makes superluminal lasers highly attractive for various sensing applications, primarily for challenging tasks such as gravitational wave detection and navigation grade rotation sensing. The realization of superluminal lasers requires the presence of a narrow dip in the center of a broad gain profile. The depth and width of the dip must be tailored carefully to produce the required dispersion profile yielding the enhanced sensitivity.
Abstract : We demonstrated that an optical laser can operate with less than 1 photons on average inside the cavity while also obtaining significant spectral narrowing of the emitted light relative to the single atom transition linewidth. We further explored the power output properties and threshold conditions of this laser. We made direct measurements that showed that the lasing frequency can be made greater than 10000 times less sensitive to the resonance frequency of the optical cavity than is the case for normal lasers or for passive optical reference cavities. Such a large reduction in sensitivity would essentially remove both thermal and technical mirror vibrations as a limitation on laser linewidth. Other studies included how phase information can be stored and manipulated inside of our laser, such that it may be possible to have both an active laser and a passive Ramsey-like sensor in the same setup. We considered the fundamental limits on the atomic quantum information that can be extracted from the laser light and found that it corresponded closely to the fundamental atomic standard quantum limit on phase estimation.
We show that the frequency of a Raman laser is highly correlated or anticorrelated with the frequency of the Raman pump laser, depending on whether the dispersion experienced by the Raman laser is positive or negative. For a subluminal laser, corresponding to a positive dispersion with a group index that is much larger than unity, the shift in its frequency is approximately the same as that in the Raman pump laser. In contrast, for a superluminal laser, corresponding to a negative dispersion with a group index that is close to zero, its frequency shifts in the direction opposite to that of the Raman pump lasers and has an amplitude that is larger by a factor approximately equaling the inverse of the group index. These findings would play a critical role in determining the maximum achievable sensitivity of sensors employing such lasers, especially under conditions where the pump laser linewidth is broadened significantly beyond the Schawlow-Townes linewidth due to classical fluctuations.
We perform a first-principles calculation of the quantum-limited laser linewidth, testing the predictions of recently developed theories of the laser linewidth based on fluctuations about the known steady-state laser solutions against traditional forms of the Schawlow-Townes linewidth. The numerical study is based on finite-difference time-domain simulations of the semiclassical Maxwell-Bloch lasing equations, augmented with Langevin force terms, and includes the effects of dispersion, losses due to the open boundary of the laser cavity, and non-linear coupling between the amplitude and phase fluctuations (α factor). We find quantitative agreement between the numerical results and the predictions of the noisy steady-state ab initio laser theory (N-SALT), both in the variation of the linewidth with output power, as well as the emergence of side-peaks due to relaxation oscillations.