Coexisting periodic attractors in injection locked diode lasers

We present experimental evidence for coexisting periodic attractors in a semiconductor laser subject to external optical injection. The coexisting attractors appear after the semiconductor laser has undergone a Hopf bifurcation from the locked steady state. We consider the single mode rate equations and derive a third order differential equation for the phase of the laser field. We then analyze the bifurcation diagram of the time periodic states in terms of the frequency detuning and the injection rate and show the existence of multiple periodic attractors.Comment: LaTex, 14 pages, 6 postscript figures include

Analytical theory of external cavity modes of a semiconductor laser with phase conjugate feedback

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Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: Theory and experiment

We analyze the dynamics of two semiconductor lasers with so-called orthogonal time-delayed mutual coupling: the dominant TE (x) modes of each laser are rotated by 90∘ (therefore, TM polarization or y) before being coupled to the other laser. Although this laser system allows for steady-state emission in either one or in both polarization modes, it may also exhibit stable time-periodic dynamics including square waveforms. A theoretical mapping of the switching dynamics unveils the region in parameter space where one expects to observe long-term time-periodic mode switching. Detailed numerical simulations illustrate the role played by the coupling strength, the mode frequency detuning, or the mode gain to loss difference. We complement our theoretical study with several experiments and measurements. We present time series and intensity spectra associated with the characteristics of the square waves and other waveforms observed as a function of the strength of the delay coupling. The experimental observations are in very good agreement with the analysis and the numerical results.Peer ReviewedPostprint (published version

Volumetry of low-contrast liver lesions with CT: Investigation of estimation uncertainties in a phantom study

Purpose: To evaluate the performance of lesion volumetry in hepatic CT as a function of various imaging acquisition parameters. Methods: An anthropomorphic abdominal phantom with removable liver inserts was designed for this study. Two liver inserts, each containing 19 synthetic lesions with varying diameter (6–40 mm), shape, contrast (10–65 HU), and both homogenous and mixed-density were designed to have background and lesion CT values corresponding to arterial and portal-venous phase imaging, respectively. The two phantoms were scanned using two commercial CT scanners (GE 750 HD and Siemens Biograph mCT) across a set of imaging protocols (four slice thicknesses, three effective mAs, two convolution kernels, two pitches). Two repeated scans were collected for each imaging protocol. All scans were analyzed using a matched-filter estimator for volume estimation, resulting in 6080 volume measurements across all of the synthetic lesions in the two liver phantoms. A subset of portal venous phase scans was also analyzed using a semi-automatic segmentation algorithm, resulting in about 900 additional volume measurements. Lesions associated with large measurement error (quantified by root mean square error) for most imaging protocols were considered not measurable by the volume estimation tools and excluded for the statistical analyses. Imaging protocols were grouped into distinct imaging conditions based on ANOVA analysis of factors for repeatability testing. Statistical analyses, including overall linearity analysis, grouped bias analysis with standard deviation evaluation, and repeatability analysis, were performed to assess the accuracy and precision of the liver lesion volume biomarker. Results: Lesions with lower contrast and size ≤10 mm were associated with higher measurement error and were excluded from further analysis. Lesion size, contrast, imaging slice thickness, dose, and scanner were found to be factors substantially influencing volume estimation. Twenty-four distinct repeatable imaging conditions were determined as protocols for each scanner with a fixed slice thickness and dose. For the matched-filter estimation approach, strong linearity was observed for all imaging data for lesions ≥20 mm. For the Siemens scanner with 50 mAs effective dose at 0.6 mm slice thickness, grouped bias was about −10%. For all other repeatable imaging conditions with both scanners, grouped biases were low (−3%–3%). There was a trend of increasing standard deviation with decreasing dose. For each fixed dose, the standard deviations were similar among the three larger slice thicknesses (1.25, 2.5, 5 mm for GE, 1.5, 3, 5 mm for Siemens). Repeatability coefficients ranged from about 8% to 75% and showed similar trend to grouped standard deviation. For the segmentation approach, the results led to similar conclusions for both lesion characteristic factors and imaging factors but with increasing magnitude in all the error metrics assessed. Conclusions: Results showed that liver lesion volumetry was strongly dependent on lesion size, contrast, acquisition dose, and their interactions. The overall performances were similar for images reconstructed with larger slice thicknesses, clinically used pitches, kernels, and doses. Conditions that yielded repeatable measurements were identified and they agreed with the Quantitative Imaging Biomarker Alliance’s (QIBA) profile requirements in general. The authors’ findings also suggest potential refinements to these guidelines for the tumor volume biomarker, especially for soft-tissue lesions

Stable microwave oscillations due to external-cavity-mode beating in laser diodes subject to optical feedback

Laser diodes subject to a delayed optical feedback may exhibit high-frequency oscillating intensities as a result of a beating between two external-cavity-modes ͑ECMs͒. We analyze the conditions for the stability of these microwave oscillations in the framework of the Lang-Kobayashi equations for a single-mode edgeemitting semiconductor laser ͓R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 ͑1980͔͒. We show that two different scenarios are possible. If the linewidth enhancement factor is relatively large (␣ϭ2 Ϫ5), the beating occurs between a stable ECM ͑mode͒ and an unstable ECM ͑antimode͒. The stability of the time-periodic solution is then limited in parameter space. But if the linewidth enhancement factor is sufficiently low (␣р␣ c Ӎ1), a beating between two stable modes is possible allowing stable high-frequency oscillating outputs

Square-wave switching in vertical-cavity surface-emitting lasers with polarization-rotated optical feedback: Experiments and simulations

We study experimentally the dynamics of vertical-cavity surface-emitting lasers (VCSELs) with polarization-rotated (PR) optical feedback, such that the natural lasing polarization of a VCSEL is rotated by 90 deg and then is reinjected into the laser. We observe noisy, square-wave-like polarization switchings with periodicity slightly longer than twice the delay time, which degrade to (or alternate with) bursts of irregular oscillations. We present results of simulations that are in good agreement with the observations. The simulations demonstrate that close to threshold the regular switching is very sensitive to noise, while well above threshold is less affected by the noise strength. The frequency splitting between the two polarizations plays a key role in the switching regularity, and we identify wide parameter regions where deterministic and robust switching can be observed.Postprint (published version

Dynamics of semiconductor lasers subject to delayed optical feedback: the short cavity regime,”

We give experimental and numerical evidence for a new dynamical regime in the operation of semiconductor lasers subject to delayed optical feedback occurring for short delay times. This short cavity regime is dominated by a striking dynamical phenomenon: regular pulse packages forming a robust low-frequency state with underlying fast, regular intensity pulsations. We demonstrate that these regular pulse packages correspond to trajectories moving on global orbits comprising several destabilized fixed points within the complicated phase space structure of this delay system. DOI: 10.1103/PhysRevLett.87.243901 PACS numbers: 42.65.Sf, 05.45.Jn, 42.55.Px Delayed feedback dominated systems are encountered extensively in the physical world and are of fundamental importance. They are found in models of diffusion and thermochemical reactions. In biology they occur in blood cell production, neural control, and drug delivery, and have applications in respiratory physiology In this paper, we present the first temporally resolved investigations of the dynamics of SLs operating in the short cavity regime (SCR). We demonstrate that this new dynamical regime is characterized by striking regular pulse packages (RPP) in the intensity dynamics of the system. Our numerical analysis demonstrates that RPP correspond to well-defined global orbits in phase space always along the same series of destabilized attractors and unstable saddle points. 243901-1 0031-9007͞01͞ 87(24)͞243901(4)$15.0

Dynamics of semiconductor lasers subject to delayed optical feedback: the short cavity regime,”

We give experimental and numerical evidence for a new dynamical regime in the operation of semiconductor lasers subject to delayed optical feedback occurring for short delay times. This short cavity regime is dominated by a striking dynamical phenomenon: regular pulse packages forming a robust low-frequency state with underlying fast, regular intensity pulsations. We demonstrate that these regular pulse packages correspond to trajectories moving on global orbits comprising several destabilized fixed points within the complicated phase space structure of this delay system. DOI: 10.1103/PhysRevLett.87.243901 PACS numbers: 42.65.Sf, 05.45.Jn, 42.55.Px Delayed feedback dominated systems are encountered extensively in the physical world and are of fundamental importance. They are found in models of diffusion and thermochemical reactions. In biology they occur in blood cell production, neural control, and drug delivery, and have applications in respiratory physiology In this paper, we present the first temporally resolved investigations of the dynamics of SLs operating in the short cavity regime (SCR). We demonstrate that this new dynamical regime is characterized by striking regular pulse packages (RPP) in the intensity dynamics of the system. Our numerical analysis demonstrates that RPP correspond to well-defined global orbits in phase space always along the same series of destabilized attractors and unstable saddle points. 243901-1 0031-9007͞01͞ 87(24)͞243901(4)$15.0