Non-Hermitian Ring Laser Gyroscopes with Enhanced Sagnac Sensitivity (1912.12067v1)

Abstract: Gyroscopes play a crucial role in many and diverse applications associated with navigation, positioning, and inertial sensing [1]. In general, most optical gyroscopes rely on the Sagnac effect -- a relativistically induced phase shift that scales linearly with the rotational velocity [2,3]. In ring laser gyroscopes (RLGs), this shift manifests itself as a resonance splitting in the emission spectrum that can be detected as a beat frequency [4]. The need for ever-more precise RLGs has fueled research activities towards devising new approaches aimed to boost the sensitivity beyond what is dictated by geometrical constraints. In this respect, attempts have been made in the past to use either dispersive or nonlinear effects [5-8]. Here, we experimentally demonstrate an altogether new route based on non-Hermitian singularities or exceptional points in order to enhance the Sagnac scale factor [9-13]. Our results not only can pave the way towards a new generation of ultrasensitive and compact ring laser gyroscopes, but they may also provide practical approaches for developing other classes of integrated sensors.

• The paper introduces a novel non-Hermitian cavity design in He-Ne ring laser gyroscopes that leverages exceptional points to amplify sensitivity to rotation-induced phase shifts.
• Experimental results reveal a square-root (√Ω) response, achieving over a fivefold increase in sensitivity compared to standard gyroscopes.
• The study employs a Jones matrix formalism to optimize mode coupling, paving the way for compact, ultra-sensitive sensors in navigation and photonics.

Overview of Non-Hermitian Ring Laser Gyroscopes with Enhanced Sagnac Sensitivity

The paper by Hokmabadi, Schumer, Christodoulides, and Khajavikhan presents a novel approach to enhancing the sensitivity of ring laser gyroscopes (RLGs) by leveraging non-Hermitian singularities, specifically exceptional points (EPs). This advancement addresses the increasing demand for ultra-sensitive navigation and inertial sensing systems by offering a more compact and sensitive design than traditional methods.

In conventional RLGs, sensitivity is typically limited by geometrical constraints, with the Sagnac effect—arising from relativistic phase shifts due to rotation—being the primary operational principle. Traditional enhancements rely on dispersive or nonlinear effects, but these are bounded by Hermitian system responses, limiting their effectiveness to linear perturbations of order ε. By contrast, non-Hermitian systems, when biased at EPs, exhibit an immensely amplified reaction to perturbations, characterized by an Nth root dependence (ε^1/N), thereby offering a promising route to circumvent existing limitations.

Theoretical Basis and Methodology

This paper introduces a modified He-Ne RLG incorporating exceptional points to achieve heightened Sagnac sensitivity. The modification involves a non-Hermitian cavity design with components such as a Faraday rotator, a half-waveplate (HWP), and Brewster windows. These elements function collectively to introduce a differential loss (Δγ) between clockwise (CW) and counterclockwise (CCW) lasing modes, a condition necessary to establish an EP. Additionally, a weakly scattering object induces coupling between these modes.

The authors employ a Jones matrix formalism to describe the polarization state transitions within the cavity, allowing for precise calculation of lasing frequencies and beat frequencies, key metrics for evaluating gyroscope performance. They particularly focus on the system's performance at an EP, where they observe a square-root response to perturbations, sharply contrasting with the linear response observed in Hermitian systems.

Results and Discussion

Experimental results corroborate the theoretical predictions by demonstrating a substantial enhancement in gyroscope sensitivity when operated at exceptional points. The Sagnac effect in the non-Hermitian RLG demonstrates a √Ω relationship compared to the Ω proportionality observed in traditional configurations. The enhanced sensitivity was demonstrated empirically, with measurements indicating a sensitivity increase of over five times that of a standard RLG for an angular velocity of 1°/s under specific operating conditions.

Additionally, by tuning the coupling strength and adjusting the HWP angle, the system remains stable near an EP. Notably, while maintaining high sensitivity, the detection limits hinge on factors such as noise level in the laser system and the intrinsic gain of the configurations.

Implications and Future Directions

The integration of exceptional points into RLGs paves the way for developing highly sensitive, compact sensors crucial for various applications, including navigation and space exploration. The paper's insights extend beyond gyroscopic measurements, suggesting broader ramifications in the fields of photonics and integrated sensors, where sensitivity is of paramount importance.

Future directions in this domain could explore optimizing non-Hermitian system stability in real-world applications, ensuring robustness to perturbations, and extending these principles to other sensing technologies. Furthermore, active techniques to dynamically control the system to remain at the EP could be critical for the feasible deployment of such sensors in practical applications.

In summary, this paper exemplifies an innovative stride in enhancing RLG sensitivity through non-Hermitian physics, promising a transformation in the design and application of optical sensing technologies.