Three-wave interaction solitons in optical parametric amplification

Ibragimov, E.; Struthers, Allan; Kaup, D. J.; Khaydarov, John; Singer, Kenneth D.

doi:10.1103/physreve.59.6122

Cited by 23 publications

(15 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1-3), for a signal pulse duration τ p = 5 ps of low peak intensity (1 W/cm 2 ) and an intensity of the continuous-wave pump field I 1 = ω 1 |A 1 | 2 of 1 MW/cm 2 , corresponding to κ ≃ 0.4656 mm −1 and δ∆ω/κ ≃ 0.0827. The numerical results of Fig.1 are with excellent accuracy reproduced by the analytical solutions (25) and (26), derived in the no-pump depletion limit. Figures 1(c) and 1(d) show the corresponding behavior, along the crystal coordinate ξ = z, of the normalized photon fluence φ 2 (ξ)/φ 2 (0) [inset of Fig.1(c)], pulse center of mass η 2 (ξ) of signal field [solid curve in Fig.1(c)], and ZB amplitude η (ξ) = [φ 2 (ξ)/φ 2 (0)] η 2 (ξ) [solid curve in Fig.1(d)].…”

Section: Zitterbewegung Of Optical Pulsessupporting

confidence: 58%

“…(7) and (8) is more involved, and is given by Eqs. (25) and (26) discussed in the next section. Here we anticipate that, in this regime, the oscillatory power transfer between the two fields is generally accompanied by an oscillatory motion of the pulse center of mass, which is reminiscent of ZB for the free relativistic Dirac electron.…”

Section: Basic Model and Quantum-optical Analogymentioning

confidence: 99%

See 1 more Smart Citation

Zitterbewegung of optical pulses in nonlinear frequency conversion

Longhi¹

2010

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

Pulse walk-off in the process of sum frequency generation in a nonlinear χ (2) crystal is shown to be responsible for pulse jittering which is reminiscent to the Zitterbewegung (trembling motion) of a relativistic freely moving Dirac particle. An analytical expression for the pulse center of mass trajectory is derived in the nopump-depletion limit, and numerical examples of Zitterbewegung are presented for sum frequency generation in periodically-poled lithium niobate. The proposed quantumoptical analogy indicates that frequency conversion in nonlinear optics could provide an experimentally accessible simulator of the Dirac equation.

show abstract

Section: Zitterbewegung Of Optical Pulsessupporting

confidence: 58%

Section: Basic Model and Quantum-optical Analogymentioning

confidence: 99%

Zitterbewegung of optical pulses in nonlinear frequency conversion

Longhi¹

2010

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

show abstract

“…(3) and (4) with the boosted initial conditions (15). The result is that steadily moving solitons are not possible.…”

Section: Investigation Of Moving Solitonsmentioning

confidence: 70%

Optical-parametric-oscillator solitons driven by the third harmonic

Lutsky

Malomed²

2004

Phys. Rev. E

View full text Add to dashboard Cite

We introduce a model of a lossy second-harmonic-generating (χ (2) ) cavity externally pumped at the third harmonic, which gives rise to driving terms of a new type, corresponding to a cross-parametric gain. The equation for the fundamental-frequency (FF) wave may also contain a quadratic self-driving term, which is generated by the cubic nonlinearity of the medium. Unlike previously studied phase-matched models of χ (2) cavities driven at the second harmonic (SH) or at FF, the present one admits an exact analytical solution for the soliton, at a special value of the gain parameter. Two families of solitons are found in a numerical form, and their stability area is identified through numerical computation of the perturbation eigenvalues (stability of the zero solution, which is a necessary condition for the soliton's stability, is investigated in an analytical form). One family is a continuation of the special analytical solution.At given values of parameters, one soliton is stable and the other one is not; they swap their stability at a critical value of the mismatch parameter. The stability of the solitons is also verified in direct simulations, which demonstrate that the unstable pulse rearranges itself into the stable one, or into a delocalized state, or decays to zero. A soliton which was given an initial boost C starts to move but quickly comes to a halt, if the boost is smaller than a critical value C cr . If C > C cr , the boost destroys the soliton (sometimes, through splitting into two secondary pulses). Interactions between initially separated solitons are investigated too. It is concluded that stable solitons always merge into a single one. In the system with weak loss, it appears in a vibrating form, slowly relaxing to the static shape. With stronger loss, the final soliton emerges in the stationary form.

show abstract

“…Compression and amplification of ultra-short laser pulses in second harmonic and sum-frequency (SF) generation in the presence of GVM was theoretically predicted [4,5] and observed in several experiments [6,7]. The conversion efficiency of generated SF pulses may be optimised [8,9,10,11,12] by operating in the soliton regime [13,14]. In fact, the temporal collision of two short soliton pulses in a quadratic nonlinear crystal may efficiently generate a short, time-compressed SF pulse [8].…”

Section: Introductionmentioning

confidence: 99%