Complex Envelopes for Oscillations in Slightly Nonlinear Systems

1971 ◽  
Vol 38 (4) ◽  
pp. 1012-1016
Author(s):  
W. H. Pierce
Keyword(s):  
Nonlinear System ◽  
Resonant Frequency ◽  
Broad Band ◽  
Method Of Averaging ◽  
Complex Envelope ◽  
High Q ◽  
Resonant Modes ◽  
Elliptical Motion ◽  
The Hilbert Transform ◽  
Simple Equations

A complex envelope f(t) is used to replace the traditional sine and cosine envelopes of the response of a sinusoidally forced, slightly nonlinear system, so that the response is y(t) = Re [f(t)ejw0t]. By setting Im [f(t)ejw0t] equal to the Hilbert transform of y(t), simple equations for the derivative of f(t) are easily obtained by the method of averaging. The approximations implicit in the method of averaging are shown to introduce broad-band filtering, whose effects can be eliminated by use of all harmonics. An example of an off-center rotary load shaken by a general elliptical motion shows how resonant modes of the device’s mount can be selectively energized at different frequencies, provided the modes have high Q and adequate separation of resonant frequency.

High- Q resonant modes in a finite array of dielectric particles

2019 ◽  
Vol 99 (3) ◽  
Author(s):  
Evgeny N. Bulgakov ◽  
Almas F. Sadreev
Keyword(s):  
High Q ◽  
Dielectric Particles ◽  
Resonant Modes

High Q merit factor, low frequency acoustic resonant modes from a Pt{100} single crystal

1996 ◽  
Vol 69 (24) ◽  
pp. 3677-3679 ◽  
Author(s):  
T. Mitrelias ◽  
S. Kelling ◽  
M. Gruyters ◽  
D. A. King
Keyword(s):  
Single Crystal ◽  
Low Frequency ◽  
High Q ◽  
Merit Factor ◽  
Resonant Modes

scholarly journals Air-Coupled and Resonant Pulse-Echo Ultrasonic Technique

Sensors ◽  
2019 ◽  
Vol 19 (10) ◽  
pp. 2221 ◽  
Author(s):  
Tomás Gómez Álvarez-Arenas ◽  
Jorge Camacho
Keyword(s):  
Resonant Frequency ◽  
Decay Time ◽  
Dead Zone ◽  
Steel Plates ◽  
Angle Of Incidence ◽  
Ultrasonic Technique ◽  
First Wall ◽  
Resonant Modes ◽  
Quality Factor Q ◽  
Pulse Echo

An ultrasonic, resonant, pulse-echo, and air-coupled nondestructive testing (NDT) technique is presented. It is intended for components, with regular geometries where it is possible to excite resonant modes, made of materials that have a high acoustic impedance (Z) and low attenuation coefficient (α). Under these conditions, these resonances will present a very large quality factor (Q) and decay time (τ). This feature is used to avoid the dead zone, produced by the echo coming from the first wall, by receiving the resonant echo from the whole specimen over a longer period of time. This echo is analyzed in the frequency domain to determine specimen resonant frequency, which can be further used to determine either velocity or thickness. Using wideband air-coupled transducers, we tested the technique on plates (steel, aluminum, and silicone rubber) by exciting the mode of the first thickness. As expected, the higher the Z and the lower the α, the better the technique performed. Sensitivity to deviations of the angle of incidence away from normal (±2°) and the possibility to generate shear waves were also studied. Then, it was tested on steel cylindrical pipes that had different wall thicknesses and diameters. Finally, the use of this technique to generate C-Scan images of steel plates with different thicknesses was demonstrated.

scholarly journals Design, Fabrication, and Characterization of a High Q Silica Nanobeam Cavity With Orthogonal Resonant Modes

2017 ◽  
Vol 9 (5) ◽  
pp. 1-9
Author(s):  
Tomohiro Tetsumoto ◽  
Hajime Kumazaki ◽  
Kentaro Furusawa ◽  
Norihiko Sekine ◽  
Takasumi Tanabe
Keyword(s):  
High Q ◽  
Resonant Modes ◽  
Fabrication And Characterization

A high-Q broad-band active inductor and its application to a low-loss analog phase shifter

1996 ◽  
Vol 44 (12) ◽  
pp. 2369-2374 ◽  
Author(s):  
H. Hayashi ◽  
M. Muraguchi ◽  
Y. Umeda ◽  
T. Enoki
Keyword(s):  
Phase Shifter ◽  
Broad Band ◽  
Active Inductor ◽  
Low Loss ◽  
High Q

scholarly journals Photonic Crystals: Shaping the Flow of Thermal Radiation

2009 ◽  
Vol 1162 ◽  
Author(s):  
Ivan Čelanović ◽  
Michael Ghebrebrhan ◽  
Yi Xiang Yeng ◽  
John Kassakian ◽  
Marin Soljačić ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Thermal Emission ◽  
Resonant Cavity ◽  
Broad Band ◽  
Selective Emitter ◽  
Spatial Properties ◽  
Resonant Modes ◽  
Thermal Emitters ◽  
Thermal Emitter ◽  
Vertical Cavity

AbstractIn this paper we explore theory, design, and fabrication of photonic crystal (PhC) based selective thermal emitters. In particular, we focus on tailoring spectral and spatial properties by means of resonant enhancement in PhC's. Firstly, we explore narrow-band resonant thermal emission in photonic crystals exhibiting strong spectral and directional selectivity. We demonstrate two interesting designs based on resonant Q-matching: a vertical cavity enhanced resonant thermal emitter and 2D silicon PhC slab Fano-resonance based thermal emitter. Secondly, we examine the design of 2D tungsten PhC as a broad-band selective emitter. Indeed, based on the resonant cavity coupled resonant modes we demonstrate a highly selective, highly-spectrally efficient thermal emitter. We show that an emitter with a photonic cut-off anywhere from 1.8 μm to 2.5 μm can be designed.

scholarly journals Ultrahigh-Q system of a few coaxial disks

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Konstantin Pichugin ◽  
Almas Sadreev ◽  
Evgeny Bulgakov
Keyword(s):  
Dielectric Resonators ◽  
Destructive Interference ◽  
High Contrast ◽  
High Q ◽  
Multi Scale ◽  
Resonant Modes ◽  
Avoided Crossing ◽  
Surrounding Space ◽  
Dielectric Disk ◽  
Q System

Abstract Resonant modes of high contrast dielectric disk have finite Q-factors in the subwavelength range due to radiation leakage into the surrounding space. That leakage can be reduced considerably (a few times) by exploiting of the mechanism of destructive interference of two modes for avoided crossing of resonances (ACR) (Rybin et al. M. V. Rybin, K. L. Koshelev, Z. F. Sadrieva, et al., “High-Q Supercavity Modes in Subwavelength Dielectric Resonators,” Phys. Rev. Lett., vol. 119, p. 243901, 2017.). In the present paper we report suppression of radiation leakage by a few orders in magnitude via the ACR in the structure of three and four different coaxial disks. For fine multi-scale tuning of disks we reveal the ultrahigh-Q resonances of order 105 for the case of three disks and of order 106 for the case of four coaxial disks of equal radii.

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