This paper is an overview of current gyroscopes and their roles based on their applications. The considered gyroscopes include mechanical gyroscopes and optical gyroscopes at macro- and micro-scale. Particularly, gyroscope technologies commercially available, such as Mechanical Gyroscopes, silicon MEMS Gyroscopes, Ring Laser Gyroscopes (RLGs) and Fiber-Optic Gyroscopes (FOGs), are discussed. The main features of these gyroscopes and their technologies are linked to their performance.

Recently, non-Hermitian Hamiltonians have gained a lot of interest, especially in optics and electronics. In particular, the existence of real eigenvalues of non-Hermitian systems has opened a wide set of possibilities, especially, but not only, for sensing applications, exploiting the physics of exceptional points. In particular, the square root dependence of the eigenvalue splitting on different design parameters, exhibited by 2 × 2 non-Hermitian Hamiltonian matrices at the exceptional point, paved the way to the integration of high-performance sensors. The square root dependence of the eigenfrequencies on the design parameters is the reason for a theoretically infinite sensitivity in the proximity of the exceptional point. Recently, higher-order exceptional points have demonstrated the possibility of achieving the nth root dependence of the eigenfrequency splitting on perturbations. However, the exceptional sensitivity to external parameters is, at the same time, the major drawback of non-Hermitian configurations, leading to the high influence of noise. In this review, the basic principles of PT-symmetric and anti-PT-symmetric Hamiltonians will be shown, both in photonics and in electronics. The influence of noise on non-Hermitian configurations will be investigated and the newest solutions to overcome these problems will be illustrated. Finally, an overview of the newest outstanding results in sensing applications of non-Hermitian photonics and electronics will be provided.

Optical gyroscopes measure the angular velocity using the Sagnac effect. However, the resonance splitting due to the Sagnac effect is directly proportional to the linear dimensions of the device. Consequently, integrated optical gyroscopes are still the subject of research. We propose the idea and the design of an anti-parity-time (APT)-symmetric optical gyroscope exhibiting a resonance splitting independent from the dimensions of the device. With a 80 μm×40 μm footprint integrated device, we demonstrated that it is possible to achieve a resonance splitting 106 times higher than the one obtained through the classical Sagnac effect. With respect to the previously proposed parity-time (PT)-symmetric gyroscope, our solution exhibits a real frequency splitting, directly measurable at the output power spectrum. Moreover, it can be kept at its exceptional point more accurately than the PT-symmetric counterpart. Finally, the anti-PT-symmetric gyroscope presented here can detect the sign of the angular velocity differently from the PT-symmetric one.

We propose an alternative readout scheme for the ultrasensitive gyroscope shown in [1], which uses the physics of the exceptional points of a PT-symmetric system to enhance the device sensitivity. In particular, we demonstrate that the full width at half maximum linewidth (ΔωFWHM) of the light exiting the ring resonator system is proportional to the square root of the rotation rate (Ω). Moreover, we design a PT-symmetric gyroscope, kept at the exceptional point (at rest) with two 100 μm-radius rings, obtaining a theoretical ΔωFWHM of 3.37ċ104 rad/s for an angular velocity of 100 °/h. One algorithm capable to keep the system at the exceptional point and another one to identify the direction of rotation are also proposed.

Non-Hermitian photonics has attracted increasing attention especially for sensing applications. Two coupled optical systems, designed to work at the exceptional point, exhibit a strong spectral response to perturbations. Due to the enhanced sensitivity of exceptional points, they have been usually suggested as perfect candidates for high resolution sensing. The drawback of these configurations is their undesired sensitivity also to external fluctuations and noise that could eliminate the advantages of exceptional points. Recently, the concept of exceptional surface has been proposed to overcome this problem. In particular, coupling two counterpropagating modes in the same structure prevents differential noise in distinct cavities from affecting the exceptional-point condition. In this work we present a new configuration based on exceptional surfaces to design an optical accelerometer. The strong spectral response guaranteed by exceptional surfaces is used here to demonstrate the enhancement of the sensitivity of a Bragg grating-based optical accelerometer, reaching a value of 3 nm/g at 0.5 g.