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arXiv:quant-ph/9706029 · Physica A Statistical Mechanics and its Applications

Light propagation in nonlinear waveguide and classical two-dimensional oscillator

A. Angelow

Published Aug 1, 1998• 8 citations
arXivHTMLPDF
DOI
10.1016/s0378-4371(98)00198-8

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1 Light Propagation in Nonlinear Waveguide and Classical Two-Dimensional Oscillator

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It has been found a solution of the equation for classical nonstationary harmonic oscillator, with time dependent frequency in integral form. It has been shown, that the quantum optical problem for propagation of electromagnetic waves in nonlinear waveguide is related to the solutions of classical nonstationary harmonic oscillator. This method could be used for obtaining other solutions of the classical harmonic oscillator, with other time dependent frequency, if we have already determined the fluctuations σq, σp and covariance cqp by some different methods. There have been found the substitutions, which allow to establish a connection between the general method of linear invariants [Malkin et.al., Phys Rev.2D (1970) 1371] and some particular cases in later papers. This gives the opportunity to present the problem with equation of two- dimensional nonstationary harmonic oscillator, which is physically more informative. 1

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In this paper, we investigate the optical analog to coherent population return (CPR) in coupled nonlinear waveguides. The nonlinearity sometimes plays a negative role in classical simulations of quantum adiabatic passages in waveguides. Nevertheless, it is interesting to note that the nonlinearity here helps simulating the adiabatic CPR technique. The CPR can still occur when the detuning (difference of the propagation constants) between the two nonlinear waveguides is moderate, which is a typical requirement of the technique. Moreover, the adiabatic process can appear when the detuning is small or zero. This is done by simply adjusting the incident light power, which is easy and of high accuracy compared with modulating the propagation constants. Therefore, the requirements towards the propagation constants of the waveguides are further relaxed in the nonlinear case. Finally, we point out that the CPR in nonlinear waveguides can be extended to design achromatic beam splitters.

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Classical Nonlinear Optics

Pierre Meystre, Murray Sargent

Springer eBooks•Jan 1, 1990•1 citation
It has been found a solution of the equation for classical nonstationary harmonic oscillator, with time dependent frequency in integral form. It has been shown, that the quantum optical problem for propagation of electromagnetic waves in nonlinear waveguide is related to the solutions of classical nonstationary harmonic oscillator. This method could be used for obtaining other solutions of the classical harmonic oscillator, with other time dependent frequency, if we have already determined the fluctuations σq, σp and covariance cqp by some different methods. There have been found the substitutions, which allow to establish a connection between the general method of linear invariants [Malkin et.al., Phys Rev.2D (1970) 1371] and some particular cases in later papers. This gives the opportunity to present the problem with equation of two- dimensional nonstationary harmonic oscillator, which is physically more informative. 1
Abstract We investigate the adiabatic evolution of light in nonlinear waveguide couplers via resonance-locked inverse engineering based on stimulated Raman adiabatic passage (STIRAP). The longitudinal varying propagation coefficients of the waveguides are designed to eliminate dynamically the nonlinear effect, which induce the non-adiabatic oscillations. We show that different light evolutions such as complete light transfer, light split and light return can be realized adiabatically with appropriate choices of the detunings even in the nonlinear regime. The features open new opportunities for the realization of all-optical nonlinear devices with high fidelity in integrated optics.
In this paper, we investigate the optical analog to coherent population return (CPR) in coupled nonlinear waveguides. The nonlinearity sometimes plays a negative role in classical simulations of quantum adiabatic passages in waveguides. Nevertheless, it is interesting to note that the nonlinearity here helps simulating the adiabatic CPR technique. The CPR can still occur when the detuning (difference of the propagation constants) between the two nonlinear waveguides is moderate, which is a typical requirement of the technique. Moreover, the adiabatic process can appear when the detuning is small or zero. This is done by simply adjusting the incident light power, which is easy and of high accuracy compared with modulating the propagation constants. Therefore, the requirements towards the propagation constants of the waveguides are further relaxed in the nonlinear case. Finally, we point out that the CPR in nonlinear waveguides can be extended to design achromatic beam splitters.