Self-Trapping of Optical Beams

Chiao, Raymond Y.; Garmire, E.; Townes, C. H.

doi:10.1103/physrevlett.13.479

Cited by 2,014 publications

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“…The nonlinear refractive index of ruby (7 = n 2 / n 0 ce 0 = 3.7 X 1(T 16 cm 2 /W, n 0 ** 1.76 [14]) gives rise to self-phase modulation [15] and self-focusing [16]. The self-phase modulation sweeps the carrier frequency of the ligh pulse along time in a sineshaped manner (pulse chirping) [17].…”

Section: Discussionmentioning

confidence: 99%

Pulse compression in a passively mode-locked ruby laser

Sperber

Penzkofer

1985

Optics Communications

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A passively mode-locked ruby laser oscillator with two saturable absorber cells is described that towards the end of the pulse train, generates picosecond pulses of about 3 ps FWHM upon weak pedestals approximately 40 ps wide. The pulse shortening in the oscillator is a combined effect of pulse chirping by self-phase modulation, pulse compression of the chirped pulses by the finite spectral gain width of the active medium, and pulse shortening by the saturable absorbers.

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Section: Discussionmentioning

confidence: 99%

Pulse compression in a passively mode-locked ruby laser

Sperber

Penzkofer

1985

Optics Communications

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“…For quasi-monochromatic waves, the two dimensional Nonlinear Schrödinger Equation (NLSE) is a precise mathematical model that describes such phenomenon. In this case, rigorous results such as the virial theorem support the fact that an initial beam having power above critical (as defined by an exact balance between self-focusing and diffraction) leads to a collapse event at finite propagation distance [1]. As the beam propagates towards the collapse point, it assumes a particular shape known as the Townes soliton solution of the NLSE [2].…”

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confidence: 96%

Collapse events of two-color optical beams

et al. 2017

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“…Thus, the observed bright solitons were found to be robust, which would not be the case in a higher-dimensional system, as they should either collapse or expand indefinitely depending on the number of atoms and the density profile. The solution that constitutes the unstable separatrix between expansion and collapse is the well-known Townes soliton [437,438].…”

Section: 42mentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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Abstract. The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45 • EP: Ermakov-Pinney (Equation)• GP: Gross-Pitaevskii (Equation)• KdV: Korteweg-de Vries (Equation)• LS: Lyapunov-Schmidt (Technique)• MT: Magnetic Trap• NLS: Nonlinear Schrödinger (Equation)• NPSE: Non-polynomial Schrödinger Equation IntroductionThe phenomenon of Bose-Einstein condensation is a quantum phase transition originally predicted by Bose [1] and Einstein [2,3] in 1924. In particular, it was shown that below a critical transition temperature T c , a finite fraction of particles of a boson gas (i.e., whose particles obey the Bose statistics) condenses into the same quantum state, known as the Bose-Einstein condensate (BEC). Although BoseEinstein condensation is known to be a fundamental phenomenon, connected, e.g., to superfluidity in liquid helium and superconductivity in metals (see, e.g., Ref.[4]), BECs were experimentally realized 70 years after their theoretical prediction: this major achievement took place in 1995, when different species of dilute alkali vapors confined in a magnetic trap (MT) were cooled down to extremely low temperatures [5][6][7], and has already been recognized through the 2001 Nobel prize in Physics [8,9]. This first unambiguous manifestation of a macroscopic quantum state in a manybody system sparked an explosion of activity, as reflected by the publication of several thousand papers related to BECs since then. Nowadays there exist more than fifty experimental BEC groups around the world, while an enormous amount of theoretical work has followed and driven the experimental efforts, with an impressive impact on many branches of Physics.From a theoretical standpoint, and for experimentally relevant conditions, the static and dynamical properties of a BEC can be described by means of an effective mean-field equation known as the Gross-Pitaevskii (GP) equation [10,11]. This is a variant of the famous nonlinear Schrödinger (NLS) equation [12] (incorporating an external potential used to confine th...

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Self-Trapping of Optical Beams

Cited by 2,014 publications

References 0 publications

Pulse compression in a passively mode-locked ruby laser

Pulse compression in a passively mode-locked ruby laser

Collapse events of two-color optical beams

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

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