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.

Lasing dynamics of super and sub luminal lasers.

A gyroscope structure with tailored local dispersion profile to enhance sensitivity is proposed, which uses lithium niobate (LiNbO3) thin film as the on-chip material of gyroscope’s resonator. A Mach–Zehnder interferometer (MZI) structure as a coupler, which induces a different reference phase shift in each arm, is inserted into the position between ring resonator and output bus waveguide. Through modulating reference phase shift in MZI, theoretical rotation sensitivity enhancement as large as one order of magnitude is presented.

On-chip tunable dispersion in a ring laser gyroscope for enhanced rotation sensing

The effect of broadened linewidth induced by dispersion on the performance of resonant optical gyroscope

We analyzed the effective scale factor of ring laser gyros with coupled cavities in a general way. The coupled cavities can be made of both an odd and even number of mirrors, or even fiber coil. Compared with the "zero-vector-area" design in previous publications, we use the propagation loss rather than transmittance and reflectivity of mirrors to characterize the coupled cavities, which are more universal and controllable. In addition, we found the area of the coupled cavities could further enhance the effective scale factor by 1+l/L, where l and L are the round-trip length of the ring lasers and the coupled cavity, respectively. Therefore, the scheme using coupled cavities to enhance the sensitivity is more practical. These findings are important to realize highly sensitive ring laser gyros.

Theoretical analysis on the rotation-induced frequency difference in ring lasers with coupled cavities.

Rigorous expressions of resonant frequency shift (RFS) in anomalous dispersion enhanced resonant optical gyroscopes (ADEROGs) are deduced without making approximation, which provides a precise theoretical guidance to achieve ultra-sensitive ADEROGs. A refractive index related modification factor is introduced when considering special theory of relativity (STR). We demonstrate that the RFS will not be "infinitely large" by using critical anomalous dispersion (CAD) and negative modification does not exist, which make the mechanism of anomalous dispersion enhancement clear and coherent. Although step change of RFS will happen when the anomalous dispersion condition varies, the amplification of RFS is limited by attainable variation of refractive index in practice. Moreover, it is shown that the properties of anomalous dispersion will influence not only the amplification of RFS, but also the detection range of ADEROGs.

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Theoretical analyses of resonant frequency shift in anomalous dispersion enhanced resonant optical gyroscopes.

A helium–neon ring laser cavity is modified by employing variable coupled passive cavities to introduce anomalous dispersion. An equivalent model for the coupled cavities is proposed, and new equations are performed. Theoretical analysis of the parameters is presented in detail, and a novel iterative method is proposed. Gyros using this ring laser are shown in different sensitivity enhancements with limited broadened passive cavity line-width, and the minimal measurable rotation rate is analyzed. The related quantum noise limited line-width is found to be broadened with limitations, which mainly depend on the round trip loss. Fluctuations are induced to analyze parameter influences on enhancements, and a novel modification method concerning mirror reflectivity is proposed for experimental setups. Finally several practical considerations are generally discussed, and some suggestions are proposed for realization. This fast light induced enhancement can be important for present gyros based on a He–Ne ring laser.

https://iopscience.iop.org/article/10.1088/2040-8978/16/12/125401/pdf

Tianliang Qu

Papers

Theoretical design of a superluminal helium–neon ring laser via coupled passive cavities