Chaos and order in second-harmonic generation: Cumulant approach

Szlachetka, P.; Grygiel, K.; Bajer, J.; Peřina, Jan

doi:10.1103/physreva.46.7311

Cited by 11 publications

(14 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This means that the parameter sensitivity of the SHG compared with the amplitude of the electric field is very high [28,29]. This parameter sensitivity of SHG dynamics confirms previous works proving the existence of chaos in this system [20,21,26]. On this matter, coherently driven second-harmonic generation within a detuned Fabry-Perot cavity is predicted to exhibit self-pulsing, period doubling and optical chaos [20].…”

Section: Resultssupporting

confidence: 71%

Study of the Transition to Instability in Second-Harmonic Generation with Scale Index Method

Behnia

Ziaei

Khodavirdizadeh

2017

IJOP

View full text Add to dashboard Cite

ABSTRACT-The emergence of secondharmonic generation (SHG) is a pivotal issue to the development of nano-optical devices and interfaces. Here, we perform a classical analysis of the SHG dynamics with the aim of determining critical values of the electric field. The signals of the SHG process are nonlinear, so it seems reasonable that chaos theory can be a suitable tool to analyze their dynamics. For this purpose the bifurcation analysis and a new measure known as the scale index were employed. Obtained results show that the dynamics approaches from stable to self-pulsing and eventually to chaos through a perioddoubling route. Moreover, the scale index can detect the critical strength of the electric field, where above it the SHG dynamics is chaotic.

show abstract

Section: Resultssupporting

confidence: 71%

Study of the Transition to Instability in Second-Harmonic Generation with Scale Index Method

Behnia

Ziaei

Khodavirdizadeh

2017

IJOP

View full text Add to dashboard Cite

show abstract

“…In this respect, the quantized SHG is a somewhat singular problem. In other quantum optical systems, for instance, for a nonlinear oscillator with l ≥ 1, typically both criteria of validity (16) and (15) give the same result.…”

Section: Quantum-classical Correspondence In Self-pulsing Regime mentioning

confidence: 84%

“…For dissipative systems with a simple attractor, the classical field intensity |z cl (t)| 2 , as well as cumulants B(t), C(t) and quantum correction Q(t) are proportional to the factor exp(−γt) and therefore, as follows from Eqs. (15) and (16) with account of Eq. (14), the 1/N -expansion is well defined only in the time interval of order of several relaxation times: t * ≃ γ −1 [19].…”

Section: /N -Expansion and Quantum-classical Correspondencementioning

confidence: 99%

Quantum-classical correspondence and nonclassical state generation in dissipative quantum optical systems

Alekseev

Alekseeva

Peřina

2000

J. Exp. Theor. Phys.

Self Cite

View full text Add to dashboard Cite

We develop a semiclassical method for the determination of the nonlinear dynamics of dissipative quantum optical systems in the limit of large number of photons N , based on the 1/N -expansion and the quantum-classical correspondence. The method has been used to tackle two problems: to study the dynamics of nonclassical state generation in higher-order anharmonic dissipative oscillators and to establish the difference between the quantum and classical dynamics of the second-harmonic generation in a self-pulsing regime. In addressing the first problem, we have obtained an explicit time dependence of the squeezing and the Fano factor for an arbitrary degree of anharmonism in the short-time approximation. For the second problem, we have established analytically a characteristic time scale when the quantum dynamics differs insignificantly from the classical one. 05.45.+b, 03.65.Sq, 42.50.Dv

show abstract

“…Historically, for the first time in the treatment of classical dynamical systems, a truncation method was used by Lorenz [2]. A similar truncation method can be used for generalized FokkerPlanck equations if we note that these equations generate a hierarchic and infinite set of ordinary differential equations for statistical cumulants [169][170][171]. The first truncation always leads to equations having the form of classical equations of motion.…”

Section: Quantum Chaosmentioning

confidence: 98%

“…The second truncation plays the role of the first quantum correction, and so on. The cumulant method has also been applied to the study of some aspects of chaos in classical and quantum mechanics [173,174] and in quantum optics [165,166,171,172]. To identify chaotic behavior of a classical dynamical system, it suffices to use the maximal Lyapunov exponent.…”

Section: Quantum Chaosmentioning

confidence: 99%