Theory of the bistable limit cycle behavior of laser diodes induced by weak optical feedback

A. Ritter; H. Haug

doi:10.1109/3.214491

Theory of laser diodes with weak optical feedback II Limit-cycle behavior, quasi-periodicity, frequency locking, and route to chaos

Journal of the Optical Society of America B ◽

10.1364/josab.10.000145 ◽

1993 ◽

Vol 10 (1) ◽

pp. 145 ◽

Cited By ~ 35

Author(s):

Alfred Ritter ◽

Hartmut Haug

Keyword(s):

Limit Cycle ◽

Optical Feedback ◽

Laser Diodes ◽

Frequency Locking ◽

Route To Chaos ◽

Limit Cycle Behavior

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Suppression of Optical Feedback in Laser Diodes Using Multilayered Broad-band Ultra-low Reflective Facets-coating

Journal of Nano- and Electronic Physics ◽

10.21272/jnep.12(2).02030 ◽

2020 ◽

Vol 12 (2) ◽

pp. 02030-1-02030-5

Author(s):

Sanjay J. Patel ◽

◽

Akshay Jariwala ◽

C. J. Panchal ◽

Vipul Kheraj ◽

...

Keyword(s):

Optical Feedback ◽

Broad Band ◽

Laser Diodes

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Limit cycle behavior of pipelined recursive digital filters

IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing ◽

10.1109/82.287006 ◽

1994 ◽

Vol 41 (5) ◽

pp. 351-355 ◽

Cited By ~ 5

Author(s):

Kyung Hi Chang ◽

W.G. Bliss

Keyword(s):

Limit Cycle ◽

Digital Filters ◽

Recursive Digital Filters ◽

Limit Cycle Behavior

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Microwave modulation of laser diodes with optical feedback

Journal of Lightwave Technology ◽

10.1109/50.76661 ◽

1991 ◽

Vol 9 (4) ◽

pp. 468-476 ◽

Cited By ~ 16

Author(s):

J. Helms ◽

K. Petermann

Keyword(s):

Optical Feedback ◽

Laser Diodes ◽

Microwave Modulation

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Modeling Unsteady Flow of a Lean Partially Premixed Flame on a Dry Low NOx Combustion System

Volume 1B: Combustion, Fuels and Emissions ◽

10.1115/gt2013-94969 ◽

2013 ◽

Author(s):

Salvatore Matarazzo ◽

Hannes Laget ◽

Evert Vanderhaegen ◽

Jim B. W. Kok

Keyword(s):

Gas Turbine ◽

Limit Cycle ◽

Gas Turbines ◽

Premixed Flame ◽

Computational Domain ◽

Pressure Oscillations ◽

Combustion Dynamics ◽

Partially Premixed ◽

Partially Premixed Flame ◽

Limit Cycle Behavior

The phenomenon of combustion dynamics (CD) is one of the most important operational challenges facing the gas turbine (GT) industry today. The Limousine project, a Marie Curie Initial Training network funded by the European Commission, focuses on the understanding of the limit cycle behavior of unstable pressure oscillations in gas turbines, and on the resulting mechanical vibrations and materials fatigue. In the framework of this project, a full transient CFD analysis for a Dry Low NOx combustor in a heavy duty gas turbine has been performed. The goal is to gain insight on the thermo-acoustic instability development mechanisms and limit cycle oscillations. The possibility to use numerical codes for complex industrial cases involving fuel staging, fluid-structure interaction, fuel quality variation and flexible operations has been also addressed. The unsteady U-RANS approach used to describe the high-swirled lean partially premixed flame is presented and the results on the flow characteristics as vortex core generation, vortex shedding, flame pulsation are commented on with respect to monitored parameters during operations of the GT units at Electrabel/GDF-SUEZ sites. The time domain pressure oscillations show limit cycle behavior. By means of Fourier analysis, the coupling frequencies caused by the thermo-acoustic feedback between the acoustic resonances of the chamber and the flame heat release has been detected. The possibility to reduce the computational domain to speed up computations, as done in other works in literature, has been investigated.

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Limit-Cycle Analysis of Three-Dimensional Flexible Shaft/Rigid Rotor/Autobalancer System With Symmetric Rigid Supports

Journal of Vibration and Acoustics ◽

10.1115/1.4032718 ◽

2016 ◽

Vol 138 (3) ◽

Cited By ~ 5

Author(s):

DaeYi Jung ◽

H. A. DeSmidt

Keyword(s):

Limit Cycle ◽

Three Dimensional ◽

Design Parameters ◽

Rigid Rotor ◽

Modal Shape ◽

Flexible Shaft ◽

Flexible Mode ◽

Automatic Balancing ◽

Rigid Supports ◽

Limit Cycle Behavior

In recent years, there has been much interest in the use of automatic balancing devices (ABD) in rotating machinery. Autobalancers consist of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance. This “automatic balancing” phenomenon occurs as a result of nonlinear dynamic interactions between the balancer and rotor wherein the balancer masses naturally synchronize with the rotor with appropriate phase to cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other undesirable nonsynchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced positions resulting in increased rotor vibration. To explore this nonsynchronous behavior of ABD, the unstable limit-cycle analysis of three-dimensional (3D) flexible shaft/rigid rotor/ABD/rigid supports described by the modal coordinates has been investigated here. Essentially, this paper presents an approximate harmonic analytical solution to describe the limit-cycle behavior of ABD–rotor system interacting with flexible shaft, which has not been fully considered by ABD researchers. The modal shape of flexible shaft is determined by using well-known fixed–fixed boundary condition due to symmetric rigid supports. Here, the whirl speed of the ABD balancer masses is determined via the solution of a nonlinear characteristic equation. Also, based upon the analytical limit-cycle solutions, the limit-cycle stability of three primary design parameters for ABD is assessed via a perturbation and Floquet analysis: the size of ABD balancer mass, the ABD viscous damping, and the relative axial location of ABD to the imbalance rotor along the shaft. The coexistence of the stable balanced synchronous condition and undesirable nonsynchronous limit-cycle is also studied. It is found that for certain combinations of ABD parameters and rotor speeds, the nonsynchronous limit-cycle can be made unstable, thus guaranteeing asymptotic stability of the synchronous balanced condition at the supercritical shaft speeds between each flexible mode. Finally, the analysis is validated through numerical simulation. The findings in this paper yield important insights for researchers wishing to utilize ABD in flexible shaft/rigid rotor systems and limit-cycle mitigation.

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