Geometric Phase Theory Research Articles

Hybrid cubic-chessboard metasurfaces for wideband angle-independent diffusive scattering and enhanced stealth.

Because of the shortcomings associated with their scattering patterns, both the chessboard and cubic phased metasurfaces show non-perfect diffusion and hence sub-optimal radar cross section reduction (RCSR) properties. This paper presents a novel and powerful hybrid RCSR design approach for diffusive scattering by combining the unique attributes of cubic phase and chessboard phase profiles. The hybrid phase distribution is achieved by simultaneously imposing two distinct phase profiles (chessboard and cubic) on the hybrid metasurface area with the aid of geometric phase theory to further enhance the diffusive scattering and RCSR. It is shown in this paper that through the integration of cubic and chessboard phase profiles, a metasurface with the hybrid phase mask successfully overcomes all the above issues and shortcomings related to the RCSR of both chessboard and cubic metasurfaces. In addition, the proposed design leverages the unique scattering properties offered by these distinct phase profiles to achieve enhanced stealth capabilities over wide frequency ranges and for large incidence angles. Simulation and measurement results show that the designed hybrid metasurfaces using the proposed strategy achieved RCSR and low-level diffused scattering patterns from 12-28 GHz (80%) for normal incidence of a far-field CP radar plane wave. The hybrid metasurface shows a stable angular diffusion and RCSR performance when the azimuthal and elevation incidence angles are in the range of 0° → ± 75° which is wider than other designs in the literature. Therefore, this work can make objects significantly less detectable in complex radar environments when enhanced stealth is required.

High Efficiency Visible Achromatic Metalens Design via Deep Learning

AbstractMetalenses with both achromatic performance and high focusing efficiency are always challenging, especially in visible range. In this work, a deep learning model is developed to accelerate the design of achromatic metalenses based on the geometric phase theory. During the building process of the phase response library and selection of the nano‐structures, converted transmission coefficients including both phase and amplitude are considered in order to ensure the achromatic focusing, as well as a high focusing efficiency. To test the performance of the design developed from the deep learning model, numerical simulations are performed in the visible wavelengths from 428 to 652 nm, which show a focal length of 266 µm with the deviation under 5%, and the average focusing efficiency reaches 52%.

Single-Layer Ultra-Wideband Multifunctional Transmissive Metasurface

The metasurface is a functional film device based on a subwavelength structure, which has a strong light field control ability and has the advantages of ultrathin, low loss, and easy manufacturing. However, realizing a multifunctional metasurface, yet simple enough to design, manufacture, and thin is still a challenge. In this article, we propose a novel metasurface with negligible thickness as a beam splitter, which can achieve half transmission and half reflection of the incident wave at the same frequency. It also controls the polarization of circularly polarized electromagnetic (EM) waves in the transmission mode. A broadband operation can be achieved based on the geometric phase theory, and the phase control can be achieved by azimuth rotation of the structure. The numerical results of the metasurface are in good agreement with the experimental results in the measured frequency range. The ultrathin multifunctional metasurface realized by the geometric phase principle provides an important stepping stone for simple optical devices and can be extended to a higher frequency range.

Vortex beam generator based on single-layer porous metasurface

Based on the geometric phase theory, a broadband terahertz wave vortex beam generator based on a transmissive plasmonic metasurface is proposed. The metasurface is composed of rectangular holes on a gold film. By deriving the relationship between the unit rotation angle and azimuth angle, arranging the rectangular holes can generate vortex beams with different topological charges. In this paper, three vortex phase plates with different topological charges are designed. The performance of metasurface vortex beam generators under normal incidence of circularly polarized beams is analyzed and discussed. In the bandwidth range of 2 THz–3 THz, the transmission efficiency can reach about 24%. The designed device is close to the transmission limit of a single-layer transmissive metasurface.

Wideband Leaky-Wave Antennas Loaded With Gradient Metasurface for Fixed-Beam Radiations With Customized Tilting Angles

We propose a hybrid dispersion compensation method to design wideband fixed-beam leaky-wave antennas (LWAs), with the tilting angle customizable in both forward and backward quadrants. In a previous work, a triangular dispersive prism constituted by metallic pins was presented to compensate for the dispersion of traditional LWAs and achieve a squint-free radiation in a relative bandwidth of 20%. However, that design suffered from the drawbacks of large geometry and limited angular range. To overcome these limitations, here a broadband gradient metasurface based on geometric phase theory is loaded in front of the prism to customize the radiation angle and reduce the total prism size. In addition, a novel ridged gap waveguide is employed to improve the linearity of LWA dispersion, which is beneficial to maintain the bandwidth of LWA with reduced size. Two examples are presented to demonstrate the excellent performance of the designed antennas. One antenna radiates at an angle of 39.5° in a squint-free bandwidth of 20%, but the prism size is decreased to a quarter of the original one, while the other realizes a broadside radiation with a squint-free bandwidth of 18%. Good agreement is exhibited between simulated and experimental results. The proposed method can be further extended to compensate for the dispersion of antenna arrays and improve the angular stability of the radiation beams in a large frequency band.

Inertial rotation measurement with atomic spins: From angular momentum conservation to quantum phase theory

Rotation measurement in an inertial frame is an important technology for modern advanced navigation systems and fundamental physics research. Inertial rotation measurement with atomic spin has demonstrated potential in both high-precision applications and small-volume low-cost devices. After rapid development in the last few decades, atomic spin gyroscopes are considered a promising competitor to current conventional gyroscopes—from rate-grade to strategic-grade applications. Although it has been more than a century since the discovery of the relationship between atomic spin and mechanical rotation by Einstein [Naturwissenschaften, 3(19) (1915)], research on the coupling between spin and rotation is still a focus point. The semi-classical Larmor precession model is usually adopted to describe atomic spin gyroscope measurement principles. More recently, the geometric phase theory has provided a different view of the rotation measurement mechanism via atomic spin. The theory has been used to describe a gyroscope based on the nuclear spin ensembles in diamond. A comprehensive understanding of inertial rotation measurement principles based on atomic spin would be helpful for future applications. This work reviews different atomic spin gyroscopes and their rotation measurement principles with a historical overlook. In addition, the spin-rotation coupling mechanism in the context of the quantum phase theory is presented. The geometric phase is assumed to be the origin of the measurable rotation signal from atomic spins. In conclusion, with a complete understanding of inertial rotation measurements using atomic spin and advances in techniques, wide application of high-performance atomic spin gyroscopes is expected in the near future.

Null phase curves and manifolds in geometric phase theory

Bargmann invariants and null phase curves are known to be important ingredients in understanding the essential nature of the geometric phase in quantum mechanics. Null phase manifolds in quantum-mechanical ray spaces are submanifolds made up entirely of null phase curves, and so are equally important for geometric phase considerations. It is shown that the complete characterization of null phase manifolds involves both the Riemannian metric structure and the symplectic structure of ray space in equal measure, which thus brings together these two aspects in a natural manner.

E. C. G. Sudarshan and symmetry in classical dynamics, optics and quantum mechanics

We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed.Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase.The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described.In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.

Geometric phases in adiabatic Floquet theory, Abelian gerbes and Cheon's anholonomy

We study the geometric phase phenomenon in the context of the adiabatic Floquet theory (so-called (t, t′) Floquet theory). A double integration appears in the geometric phase formula because of the presence of two time variables within the theory. We show that the geometric phases are then identified with horizontal lifts of surfaces in an Abelian gerbe with connection, rather than with horizontal lifts of curves in an Abelian principal bundle. This higher degree in the geometric phase gauge theory is related to the appearance of changes in the Floquet blocks at the transitions between two local charts of the parameter manifold. We present the physical example of a kicked two-level system where the changes are involved by a Cheon's anholonomy. In this context, the analogy between the usual geometric phase theory and the classical field theory also provides an analogy with the classical string theory.

Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators

The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with N-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal Stiefel U(N) bundle over a Grassmann manifold. Most significantly, for an arbitrary initial state, this holonomy captures the inherent geometric feature of the state evolution that may not be cyclic. Moreover, a rigorous theory of geometric phase in the evolution of the eigenspace of an adiabatic action operator is also formulated, with the corresponding holonomy being elaborated by a pullback U(N) bundle.

Control of a planar space robot: Theory and experiments

In this paper the attitude control problem of planar space robot is addressed and new feedback control scheme is proposed. Since control laws are synthesized via theory of geometric phase, the proposed control laws contain smooth functions of states and time. The usefulness and validity of this control scheme can be demonstrated by hardware experiments. In experiments to simulate the space environment prototype of the planar space robot is floated by air on the horizontal plane. Experimental results show that the proposed smooth time-varying control laws stabilize the attitude of the planar space robot sufficiently.

Bargmann invariants, null phase curves, and a theory of the geometric phase

We present a theory of the geometric phase based logically on the Bargmann invariant of quantum mechanics, and null phase curves in ray space, as the fundamental ingredients. Null phase curves are themselves defined entirely in terms of the (third order) Bargmann invariant, and it is shown that these are the curves natural to geometric phase theory, rather than geodesics used in earlier treatments. The natural symplectic structure in ray space is seen to play a crucial role in the definition of the geometric phase. Logical consistency of the formulation is explicitly shown, and the principal properties of geometric phases are deduced as systematic consequences.

Direct way to observe the geometric phase in nonlinear coupled oscillators

We apply the geometric phase theory to the dissipative system of a set of nonlinear coupled oscillators. We found an area theorem for the geometric phase, which provides a direct and simple geometric method for observing the geometric phase of this system. The area theorem shows evidence that the geometric phase is related to certain dynamical features of the systems.