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Journal of the Optical Society of America B

Theoretical studies for special states of cascaded quadratic nonlinear effects

Xueming Liu, Mingde Zhang

Published Nov 1, 2001• 4 citations
Publisher

Abstract

From the viewpoint of photon flux, the evolution of phases and intensities in the eigenmode state in three-wave mixing (TWM) is studied, and the requirements for the initial phases and incident intensities in this state are derived. Another special state in which there is an exchange of intensities without a phase change in the TWM is also investigated, for the first time to the authors’ knowledge. By use of the two special states of cascaded quadratic nonlinear effects, an all-optical switch based on the push–pull Sagnac loop is proposed, and its properties are calculated. The numerical results show that the switch is quite stable, and the intensity and phase of the output signal can easily be established and controlled.

DOI
10.1364/josab.18.001659

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From the viewpoint of photon flux, the evolution of phases and intensities in the eigenmode state in three-wave mixing (TWM) is studied, and the requirements for the initial phases and incident intensities in this state are derived. Another special state in which there is an exchange of intensities without a phase change in the TWM is also investigated, for the first time to the authors’ knowledge. By use of the two special states of cascaded quadratic nonlinear effects, an all-optical switch based on the push–pull Sagnac loop is proposed, and its properties are calculated. The numerical results show that the switch is quite stable, and the intensity and phase of the output signal can easily be established and controlled.
By employing the concept of photon flux,the evolution of the phase and photon flux in the eigenmode state in three-wave mixing,and the requirements for the initial phase and photon flux in this state,are studied in the paper.A special state in which there are only exchanges of the photon flux but no phase variations in the three-wave mixing process is investigated.An all-optical switch based on the eigenmode pushpull nonlinear-optical-mirror is presented,and the properties of this all-optical switch are numerically calculated.The numerical results show that the performance stability is extremely good,and the intensity and phase of the output signal beams can be easily realized and controlled.
Nonlinear optical effects in quadratic nonlinear mediums for the traditional frequency conversion generally involve two or three incident optical waves and transfer the power of the input signal wavelength to another new generated wavelength. The authors find that bidirectional power swapping can be carried out by proper waveguide length and power arrangement when two signals and two continuous-wave pumps simultaneously take part in the quadratic nonlinear interactions. Theoretical analyses referring to four incident optical waves are presented, taking into account the cascaded sum- and difference-frequency generation in a periodically poled lithium niobate waveguide. We apply such theory to ultrafast data information swapping and derive analytical solutions clearly indicating the swapping condition. An example of bidirectional ultrafast data information swapping is demonstrated.
Abstract We report a theoretical study about the two- and three-mode intensity-difference squeezing inside an atom-like optical cavity. A cascaded parametric amplification four-wave mixing process is considered, and the cavity dressing and ‘dressing-like’ effects with different nonlinear coefficients affecting the degree of squeezing of the fluctuation spectra are researched. The altering of the nonlinear coupling coefficient changes the relationship between the cavity dressing and ‘dressing-like’ effects, which determines the squeezing degree and results in a new type of multi-dip squeezing and double-peak anti-squeezing.
A comprehensive analytical approach to scalar and vectorial interaction in cascaded quadratic nonlinearities is presented. Exact formulas for the intensity as well as the phase modulation in dependence on all conceivable control parameters are derived, provided that group-velocity dispersion, diffraction, and pulse walk off can be neglected. The first two constraints are uncritical as far as channel waveguides and thin bulk crystals are concerned. Particular emphasis is paid to a detailed study of the phase evolution in order to identify optimum conditions for an almost homogeneous phase shift across an entire pulse which is in contrast to the generation of a large chirp in cubic nonlinear materials. Moreover, the general results are simplified to relevant limiting cases where simple analytical formulas emerge for the amplitude and phase modulation. The analytical results are used for a classification of all-optical effects based on cascading. Optimum conditions for picosecond modulation processes are discussed. \textcopyright{} 1996 The American Physical Society.
We theoretically analyze a new class of aperiodic phase mismatch. The phase-matching function that is chosen depends on the calculated second-harmonic amplitude generated in the device during the propagation of the fundamental beam at given input intensity and wavelength. We show that, in such a configuration, the fields evolve toward the eigenmodes of a χ(2) two-wave mixing process. Hence a constant pump and an enhanced nonlinear phase shift that grows linearly with propagation length are obtained. We also discuss the feasibility of this scheme that provides an alternative approach for the realization of optical switching devices or Kerr-effect compensators.
In a search for all-optical signal processing elements operating at a picosecond time scale nonlinear phenomena in quadratic media, extensively studied since many years in a different context were revisited lately. However, all devices proposed and implemented to date (see [1,2] and Refs, therein) have certain drawbacks complicating their use as all-optical amplifying/switching devices, viz., low amplification because of a strong control signal in intensity-controlled devices, smooth switching characteristics of Mach-Zehnder interferometers, and a requirement of fast phase control in phase-sensitive devices [3]. A key requirement of all devices proposed until now is the coherence of pump and signal beams because the χ(2)-process strongly depends on the relative phase. Here we demonstrate that this phase-insensitive amplification/switching can be achieved by a three wave interaction even with reduced pump power requirements. In what follows we focus on the so-called vectorial or type II SHG where two orthogonally polarized fundamental frequency (FF) components A1 and A2 interact with the only second harmonic (SH) wave B polarized parallel to one of the fundamentals [2].