scholarly journals LAMBERT FUNCTION METHODs TO STUDY LASER DYNAMICS WITH TIME-DELAYED FEEDBACK

2017 ◽  
Vol 57 (6) ◽  
pp. 399
Author(s):  
Yogesh N Joglekar ◽  
Gautam Vemuri ◽  
Andrew Wilkey
Keyword(s):  
Semiconductor Lasers ◽  
Optical Feedback ◽  
Single Equation ◽  
Lambert W Function ◽  
Rate Equations ◽  
Lambert Function ◽  
Laser Dynamics ◽  
Delayed Differential Equations ◽  
Time Delayed Feedback ◽  
Model Semiconductor

<p><!--StartFragment-->Time-delayed differential equations arise frequently in the study of nonlinear dynamics of lasers with optical feedback and because the analytical solution of such equations can be intractable, one resorts to numerical methods. In this manuscript, we show that under some conditions, the rate equations model that is used to model semiconductor lasers with feedback can be analytically solved by using the Lambert W function. In particular, we discuss the conditions under which the coupled rate equations for the intracavity electric field and carrier inversion can be reduced to a single equation for the field, and how this single rate equation can be cast in a form that is amenable to the use of the Lambert W function.<!--EndFragment--></p>

Effect of Spontaneous Emission Noise and Modulation on Semiconductor Lasers Near Threshold with Optical Feedback

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4123-4138 ◽  
Author(s):  
Wing-Shun Lam ◽  
Parvez N. Guzdar ◽  
Rajarshi Roy
Keyword(s):  
Semiconductor Lasers ◽  
Spontaneous Emission ◽  
Quantum Noise ◽  
Optical Feedback ◽  
Dynamical Behavior ◽  
Threshold Current ◽  
Rate Equations ◽  
Simple Explanation ◽  
Feedback Strength ◽  
Near Threshold

The dynamical behavior of power dropouts in a semiconductor laser with optical feedback, pumped near threshold current, is strongly influenced by quantum noise. This is clearly demonstrated by experiments with modulations on the pumping current or the feedback strength. For the cases without modulation and with only current modulation, the dropouts occur randomly. However the feedback strength modulation locks the dropout events periodically. By numerically modeling these three cases using the Lang–Kobayashi equations with a stochastic term to take into account spontaneous emission noise, it is shown that the observed behavior of the dropouts can be readily reproduced for all three cases. Noise plays a signifcant role in explaining the observed dropout events. A simple explanation of the observed dropout phenomenon is presented, based on the adiabatic motion of the ellipse formed by the steady state solutions of the rate equations due to slow time modulations of the injection current or the feedback strength.

scholarly journals Class-C semiconductor lasers with time-delayed optical feedback

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180124 ◽  
Author(s):  
Benjamin Lingnau ◽  
Jonas Turnwald ◽  
Kathy Lüdge
Keyword(s):  
Semiconductor Lasers ◽  
Optical Feedback ◽  
Equation System ◽  
Delay Systems ◽  
Dephasing Time ◽  
Laser Dynamics ◽  
Class B ◽  
Class C ◽  
Numerical Bifurcation ◽  
Delayed Optical Feedback

We perform a linear stability analysis and numerical bifurcation diagrams of a class-C laser with time-delayed optical feedback. We employ a rate equation system based on the Maxwell–Bloch equations, and study the influence of the dephasing time on the laser dynamics. We find a stabilizing effect of an intermediate dephasing time, i.e. when moving from a class-B to a class-C laser. At long dephasing times, a destabilization of the laser solution occurs by a feedback-induced unlocking of Rabi oscillations at the second laser threshold. We predict an optimum resistance to time-delayed optical feedback for dephasing times close to the photon cavity lifetime. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

scholarly journals ENTRAINMENT OF OPTICAL LOW-FREQUENCY FLUCTUATIONS IS ENHANCED BY COUPLING

2003 ◽  
Vol 03 (02) ◽  
pp. L127-L136 ◽  
Author(s):  
J. M. BULDÚ ◽  
J. GARCÍA-OJALVO ◽  
M. C. TORRENT ◽  
RAÚL VICENTE ◽  
TONI PÉREZ ◽  
...  
Keyword(s):  
Semiconductor Lasers ◽  
Optical Feedback ◽  
Low Frequency ◽  
Rate Equations ◽  
Differential Rate ◽  
Frequency Fluctuations ◽  
The One ◽  
Delay Differential ◽  
Low Frequency Power

The control of the low-frequency fluctuations exhibited by two mutually coupled semiconductor lasers is studied experimentally and numerically. We observe that coupling enhances the response of the system to a weak periodic modulation of the injection current of one of the lasers, leading to a highly efficient entrainment of the synchronized low-frequency power dropouts to the external periodic driving. We compare the quality of the entrainment with the one obtained in a single semiconductor laser with optical feedback, showing the beneficial role of coupling in this pursuit. The experimental observations are satisfactorily reproduced by numerical simulations of a set of coupled delay-differential rate equations.

Noise characteristics in line-narrowed semiconductor lasers with optical feedback

1981 ◽  
Vol 17 (19) ◽  
pp. 677 ◽  
Author(s):  
L. Goldberg ◽  
A. Dandridge ◽  
R.O. Miles ◽  
T.G. Giallorenzi ◽  
J.F. Weller
Keyword(s):  
Semiconductor Lasers ◽  
Optical Feedback ◽  
Noise Characteristics

Analysis of DFB semiconductor lasers with external optical feedback

1988 ◽  
Vol 24 (9) ◽  
pp. 509 ◽  
Author(s):  
J.L. Beylat ◽  
J. Jacquet
Keyword(s):  
Semiconductor Lasers ◽  
Optical Feedback

Spectral linewidth reduction in semiconductor lasers by an external cavity with weak optical feedback

1983 ◽  
Vol 19 (22) ◽  
pp. 938 ◽  
Author(s):  
E. Patzak ◽  
H. Olesen ◽  
A. Sugimura ◽  
S. Saito ◽  
T. Mukai
Keyword(s):  
Semiconductor Lasers ◽  
Optical Feedback ◽  
External Cavity ◽  
Spectral Linewidth

Spectral characteristics of semiconductor lasers with optical feedback

1982 ◽  
Vol 18 (4) ◽  
pp. 555-564 ◽  
Author(s):  
L. Goldberg ◽  
H. Taylor ◽  
A. Dandridge ◽  
J. Weller ◽  
R. Miles
Keyword(s):  
Semiconductor Lasers ◽  
Optical Feedback ◽  
Spectral Characteristics

Multi-target ranging using optical reservoir computing approach in the laterally coupled semiconductor lasers with self-feedback

2021 ◽  
Author(s):  
Dong-Zhou Zhong ◽  
Zhe Xu ◽  
Ya-Lan Hu ◽  
Ke-Ke Zhao ◽  
Jin-Bo Zhang ◽  
...  
Keyword(s):  
Semiconductor Lasers ◽  
Hilbert Transform ◽  
Optical Feedback ◽  
Optical Injection ◽  
Reservoir Computing ◽  
Probe Signal ◽  
Laser Array ◽  
Target Ranging ◽  
Relative Errors ◽  
Computing Approach

Abstract In this work, we utilize three parallel reservoir computers using semiconductor lasers with optical feedback and light injection to model radar probe signals with delays. Three radar probe signals are generated by driving lasers constructed by a three-element lase array with self-feedback. The response lasers are implemented also by a three-element lase array with both delay-time feedback and optical injection, which are utilized as nonlinear nodes to realize the reservoirs. We show that each delayed radar probe signal can well be predicted and to synchronize with its corresponding trained reservoir, even when there exist parameter mismatches between the response laser array and the driving laser array. Based on this, the three synchronous probe signals are utilized for ranging to three targets, respectively, using Hilbert transform. It is demonstrated that the relative errors for ranging can be very small and less than 0.6%. Our findings show that optical reservoir computing provides an effective way for applications of target ranging.

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