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- G Kozyreff, A G Vladimirov, P Mandel
- Physical review. E, Statistical, nonlinear, and…
- 2001

We study the dynamics of an array of single mode semiconductor lasers globally but weakly coupled by a common external feedback mirror and by nearest neighbor interactions. We seek to determine the conditions under which all lasers of the array are in phase, whether in a steady, periodic, quasiperiodic, or chaotic regime, in order to maximize the output far… (More)

- Dmitry Puzyrev, Serhiy Yanchuk, A. G. Vladimirov, S. V. Gurevich
- SIAM J. Applied Dynamical Systems
- 2014

We perform bifurcation analysis of plane wave solutions in a one-dimensional complex cubic-quintic Ginzburg–Landau equation with delayed feedback. Our study reveals how multistability and snaking behavior of plane waves emerge as time delay is introduced. For intermediate values of the delay, bifurcation diagrams are obtained by a combination of analytical… (More)

- S Slepneva, B Kelleher, B O'Shaughnessy, S P Hegarty, A G Vladimirov, G Huyet
- Optics express
- 2013

An analysis of the dynamical features in the output of a Fourier Domain Mode Locked laser is presented. An experimental study of the wavelength sweep-direction asymmetry in the output of such devices is undertaken. A mathematical model based on a set of delay differential equations is developed and shown to agree well with experiment.

- M Tlidi, A G Vladimirov, D Pieroux, D Turaev
- Physical review letters
- 2009

We study the properties of 2D cavity solitons in a coherently driven optical resonator subjected to a delayed feedback. The delay is found to induce a spontaneous motion of a single cavity soliton that is stationary and stable otherwise. This behavior occurs when the product of the delay time and the feedback strength exceeds some critical value. We derive… (More)

- Andrei G Vladimirov, John M McSloy, Dmitry V Skryabin, William J Firth
- Physical review. E, Statistical, nonlinear, and…
- 2002

Using analytical and numerical approaches we study clusters of the two-dimensional localized structures of light excited in the externally driven optical cavities. Stability and instability properties of clusters of two, three, and four structures are analyzed in detail. We develop a technique for calculation of the expression for the interaction potential… (More)

- A G Vladimirov, D V Skryabin, G Kozyreff, Paul Mandel, Mustapha Tlidi
- Optics express
- 2006

We consider a passive optical cavity containing a photonic crystal and a purely absorptive two-level medium. The cavity is driven by a superposition of two coherent beams forming a periodically modulated pump. Using a coupled mode reduction and direct numerical modeling of the full system we demonstrate the existence of bistability between uniformly… (More)

- A Yulin, Dmitry V Skryabin, A Vladimirov
- Optics express
- 2006

We study temporal modulational instability of spatial discrete solitons in waveguide arrays with group velocity dispersion (GVD). For normal GVD we report existence of the strong 'neck'-type instability specific for the discrete solitons. For anomalous GVD the instability leads to formation of the mixed discrete-continuous spatio-temporal quasi-solitons.… (More)

- M Tlidi, K Staliunas, K Panajotov, A G Vladimirov, M G Clerc
- Philosophical transactions. Series A…
- 2014

Localized structures (LSs) in dissipative media appear in various fields of natural science such as biology, chemistry, plant ecology, optics and laser physics. The proposal for this Theme Issue was to gather specialists from various fields of nonlinear science towards a cross-fertilization among active areas of research. This is a cross-disciplinary area… (More)

- D Turaev, A G Vladimirov, S Zelik
- Physical review letters
- 2012

We study the interaction of well-separated oscillating localized structures (oscillons). We show that oscillons emit weakly decaying dispersive waves, which lead to the formation of bound states due to harmonic synchronization. We also show that in optical applications the Andronov-Hopf bifurcation of stationary localized structures leads to a drastic… (More)

- Andrei G Vladimirov, Dmitry Turaev, Gregory Kozyreff
- Optics letters
- 2004

We propose a new model for passive mode locking that is a set of ordinary delay differential equations. We assume a ring-cavity geometry and Lorentzian spectral filtering of the pulses but do not use small gain and loss and weak saturation approximations. By means of a continuation method, we study mode-locking solutions and their stability. We find that… (More)