We investigate the modal characteristics of coupled-mode guiding structures in which the supported eigenmodes coalesce; the condition we refer to as an exceptional point of degeneracy (EPD). EPD is a point in a system parameter space at which the system eigenmodes coalesce in both their eigenvalues and eigenvectors, where the number of coalescing eigenmodes at the EPD defines the order of the degeneracy. First, we investigate the prospects of gain/loss balance and how it is related to realizing an EPD. Under geometrical symmetry in coupled resonators or coupled waveguides such scheme is often attributed to PT-symmetry; however, we generalize the concept of PT-symmetry to coupled waveguides exhibiting EPDs that do not necessarily have perfect geometrical symmetry. Secondly, we explore the conditions that lead to the existence of EPDs in periodically coupled waveguides that may be lossless and gainless. In general, we investigate properties associated to the emergence of EPDs in various cases: i) uniform, and ii) periodic, lossy or lossless, coupled-mode structures. Generally, the EPD condition is very sensitive to perturbations; however, it was shown recently with experimental and theoretical studies that EPDs' unconventionai properties exist even in the presence of loss and fabrication errors. Extraordinary properties of such systems at EPDs, such as the giant scaling of the quality factor and the high sensitivity to perturbation, provide opportunities for various applications in traveling wave tubes, pulse compressors and generators, oscillators, switches, modulators, lasers, and extremely sensitive sensors.
more »
« less
Sensing with exceptional points in coupled resonator or waveguide systems
The physics of exceptional points leads to very high sensitivity because the perturbation of an exceptionally degenerate state is highly sensitive to a system’s perturbation. This property is indeed not shared with nondegenerate systems, and it relies in the fractional power expansion (Puiseux series) describing the perturbation of eigenvalues and eigenvectors. We discuss how this property is met in systems made of coupled resonators and with coupled modes in waveguides, whose eigenvalues are the resonant frequencies and the wavenumbers, respectively. We will also discuss the experimental implementation of this principle in unstable nonlinear systems to build extremely sensitive saturated oscillators.
more »
« less
- Award ID(s):
- 1711975
- NSF-PAR ID:
- 10421530
- Editor(s):
- Shahriar, Selim M.; Scheuer, Jacob
- Date Published:
- Journal Name:
- Proceedings Volume PC12447, Quantum Sensing, Imaging, and Precision Metrology; PC1244724 (2023)
- Page Range / eLocation ID:
- SPIE Quantum West, San Francisco, held in Jan 2023
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We review and explore sensor applications based on electromagnetic systems operating near an exceptional point of degeneracy (EPD). The EPD is defined as the point at which the system eigenmodes coalesce in both their eigenvalues and eigenvectors varying a system parameter. Sensors based on EPDs show sensitivity proportional to δ 1/m , where δ is a perturbation of a system parameter and m is the order of the EPD. EPDs manifest in PT-symmetric systems or periodic systems that can be periodic in either time or space. We review all the methods to obtain EPD based sensors, and we focus on two classes of ultra-sensitive EPD systems: i) periodic linear time-varying single oscillators, and ii) optical gyroscopes based on a modified coupled resonators optical waveguide (CROW) exhibiting 4th order EPD.more » « less
-
Abstract Animals use a diverse array of motion to feed, escape predators, and reproduce. Linking morphology, performance, and fitness is a foundational paradigm in organismal biology and evolution. Yet, the influence of mechanical relationships on evolutionary diversity remains unresolved. Here, I focus on the many-to-one mapping of form to function, a widespread, emergent property of many mechanical systems in nature, and discuss how mechanical redundancy influences the tempo and mode of phenotypic evolution. By supplying many possible morphological pathways for functional adaptation, many-to-one mapping can release morphology from selection on performance. Consequently, many-to-one mapping decouples morphological and functional diversification. In fish, for example, parallel morphological evolution is weaker for traits that contribute to mechanically redundant motions, like suction feeding performance, than for systems with one-to-one form–function relationships, like lower jaw lever ratios. As mechanical complexity increases, historical factors play a stronger role in shaping evolutionary trajectories. Many-to-one mapping, however, does not always result in equal freedom of morphological evolution. The kinematics of complex systems can often be reduced to variation in a few traits of high mechanical effect. In various different four-bar linkage systems, for example, mechanical output (kinematic transmission) is highly sensitive to size variation in one or two links, and insensitive to variation in the others. In four-bar linkage systems, faster rates of evolution are biased to traits of high mechanical effect. Mechanical sensitivity also results in stronger parallel evolution—evolutionary transitions in mechanical output are coupled with transition in linkages of high mechanical effect. In other words, the evolutionary dynamics of complex systems can actually approximate that of simpler, one-to-one systems when mechanical sensitivity is strong. When examined in a macroevolutionary framework, the same mechanical system may experience distinct selective pressures in different groups of organisms. For example, performance tradeoffs are stronger for organisms that use the same mechanical structure for more functions. In general, stronger performance tradeoffs result in less phenotypic diversity in the system and, sometimes, a slower rate of evolution. These macroevolutionary trends can contribute to unevenness in functional and lineage diversity across the tree of life. Finally, I discuss how the evolution of mechanical systems informs our understanding of the relative roles of determinism and contingency in evolution.more » « less
-
We investigate wave properties in coupled transmission lines (CTLs) under a special condition known as the exceptional point of degeneracy (EPD) at which two or more of the supported eigenmodes of the system coalesce. At an EPD, not only the eigenvalues (resonances or wavenumbers) of the system (a resonator or a waveguide) coalesce but also the eigenvectors (polarization states) coalesce, and the number of coalescing eigenmodes defines the order of the degeneracy. We investigate different structures, either periodic or uniform CTLs, that are capable of exhibiting EPDs in their dispersion diagram. Secondly, we show an experimental verification of the existence of EPDs through measuring the dispersion of microstrip-based CTLs in the microwave spectrum. For antenna array configurations, we discuss the effect of CTLs radiative and dissipative losses on EPDs and how introducing gain to the CTLs compensate for such losses restoring the EPD in a fully radiating array, in what we define as the gain and distributed-radiation balance regime. Therefore, we show how to obtain large linear and planar arrays that efficiently generate microwave oscillations, and by spatial combination they are able to generate collimated beams with large radiation intensity. Finally, we show other promising applications based on the concept of EPDs in ultra-sensitive sensors or reconfigurable antennas.more » « less
-
In this work we consider a new class of oscillatory instabilities that pertain to thermocapillary destabilization of a liquid film heated by a solid substrate. We assume the substrate thickness and substrate–film thermal conductivity ratio are large so that the effect of substrate thermal diffusion is retained at leading order in the long-wave approximation. As a result, the system dynamics is described by a nonlinear partial differential equation for the film thickness that is non-locally coupled to the full substrate heat equation. Perturbing about a steady quiescent state, we find that its stability is described by a non-self-adjoint eigenvalue problem. We show that, under appropriate model parameters, the linearized eigenvalue problem admits complex eigenvalues that physically correspond to oscillatory (in time) instabilities of the thin-film height. As the principal results of our work, we provide a complete picture of the susceptibility to oscillatory instabilities for different model parameters. Using this description, we conclude that oscillatory instabilities are more relevant experimentally for films heated by insulating substrates. Furthermore, we show that oscillatory instability where the fastest-growing (most unstable) wavenumber is complex, arises only for systems with sufficiently large substrate thicknesses. Finally, we discuss adaptation of our model to a practical setting and make predictions of conditions at which the reported instabilities can be observed.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1117/12.2657395
