Stationary spatial patterns in passive optical systems: Two-level atoms

Lugiato, L. A.; Oldano, C.

doi:10.1103/physreva.37.3896

Cited by 115 publications

(53 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One of the most extensively studied systems has been photorefractive oscillators, where the theoretical background was set out [26], complicated structures experimentally observed [27,28] and order parameter equations derived [29]. Intensive studies of pattern formation in passive, driven, nonlinear Kerr resonators were also performed [30][31][32][33]. Also, the patterns in optical parametric oscillators received a lot of attention.…”

Section: Historical Surveymentioning

confidence: 99%

Transverse Patterns in Nonlinear Optical Resonators

Staliūnas

Sánchez‐Morcillo

2003

Springer Tracts in Modern Physics

176

156

View full text Add to dashboard Cite

This book is devoted to the formation and dynamics of localized structures (vortices, solitons) and of extended patterns (stripes, hexagons, tilted waves) in nonlinear optical resonators such as lasers, optical parametric oscillators, and photorefractive oscillators. Theoretical analysis is performed by deriving order parameter equations, and also through numerical integration of microscopic models of the systems under investigation. Experimental observations, and possible technological implementations of transverse optical patterns are also discussed. A comparison with patterns found in other nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is given.

show abstract

Section: Historical Surveymentioning

confidence: 99%

Transverse Patterns in Nonlinear Optical Resonators

Staliūnas

Sánchez‐Morcillo

2003

Springer Tracts in Modern Physics

176

156

View full text Add to dashboard Cite

show abstract

“…H(z) = e hxxz e hxyz − e −hxyz e hyxz − e −hyxz e hyy z (18) This matrix extends the scalar transformation used by Lugiato and Oldano in their original paper [41], devoted to the study of stationary spatial patterns in optical systems with two-level atoms, to a vectorial case. It is easy to verify that H(0) is the identity matrix while H(L) = RM R −1 and thus all the elements of the matrix h ij can be explicitly calculated:…”

Section: Appendixmentioning

confidence: 99%

“…[41], if p and δ are small parameters (of the order of the transmittivity T=1-r of the mirror) one can calculate a set of first order (in T) equations by expanding all coefficients up to this order. After long but straightforward calculations, the final result is a set of coupled equations for the vector A ′ = [A x , A y ] T , that still contains both ∂ z and ∂ t operators, but includes the boundary conditions.…”

Section: Appendixmentioning

confidence: 99%

Phase-locked spatial domains and Bloch domain walls in type-II optical parametric oscillators

Izús

Miguel²,

Santagiustina³

2001

Phys. Rev. E

View full text Add to dashboard Cite

We study the role of transverse spatial degrees of freedom in the dynamics of signal-idler phase locked states in type-II Optical Parametric Oscillators. Phase locking stems from signal-idler polarization coupling which arises if the cavity birefringence and/or dichroism is not matched to the nonlinear crystal birefringence. Spontaneous Bloch domain wall formation is theoretically predicted and numerically studied. Bloch walls connect, by means of a polarization transformation, homogeneous regions of self-phase locked solutions. The parameter range for their existence is analytically found. The polarization properties and the dynamics of walls in one-and two transverse spatial dimensions is explained. Transition from Bloch to Ising walls is characterized, the control parameter being the linear coupling strength. Wall dynamics governs spatiotemporal dynamical states of the system, which include transient curvature driven domain growth, persistent dynamics dominated by spiraling defects for Bloch walls, and labyrinthine pattern formation for Ising walls.

show abstract

“…Many contexts for optical-switching [6,7] and optical-memory [8] applications are based upon bistable dynamics, where the system's input-output curve has a characteristic "S" shape. The origin of these hysteretic response curves tends to lie in external boundary conditions, typically cavity feedback.…”

Section: Introductionmentioning

confidence: 99%

“…This intrinsic phenomenon [12] is potentially useful for switching applications exploiting spatial solitons in planar waveguides [13], as opposed to cavity solitons [6][7][8]14]. For a wide class of nonlinearity, there is often a parameter regime where one finds the coexistence of degenerate bright solitons -that is, beam solutions with different propagation constants but the same power [15,16].…”

mentioning

confidence: 99%

Bistable dark solitons of a cubic-quintic Helmholtz equation

2010

View full text Add to dashboard Cite

We report, to the best of our knowledge, the first exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field, and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and non-degenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit.We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.

show abstract

Stationary spatial patterns in passive optical systems: Two-level atoms

Cited by 115 publications

References 13 publications

Transverse Patterns in Nonlinear Optical Resonators

Transverse Patterns in Nonlinear Optical Resonators

Phase-locked spatial domains and Bloch domain walls in type-II optical parametric oscillators

Bistable dark solitons of a cubic-quintic Helmholtz equation

Contact Info

Product

Resources

About