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Optics Express

Exact analytical solutions and their applications for interacting waves in quadratic nonlinear medium

Xueming Liu, Hanyi Zhang, Mingde Zhang

Published Jan 14, 2002• 26 citations
Publisher

Abstract

The exact analytical solutions for the interacting waves in the quadratic nonlinear medium with the periodic structure are detailedly derived and obtained, and the properties of solutions are analyzed. Three applicable examples employing the exact solutions in the all-optical processing are given and analyzed. The optimized results show that the phase of signal can obviously be increased by proper choosing k, and that the intensity of pump can greatly be decreased in the all-optical switching by means of optimizing k, increasing medium length, and choosing sum-frequency generation.

DOI
10.1364/oe.10.000083

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The exact analytical solutions for the interacting waves in the quadratic nonlinear medium with the periodic structure are detailedly derived and obtained, and the properties of solutions are analyzed. Three applicable examples employing the exact solutions in the all-optical processing are given and analyzed. The optimized results show that the phase of signal can obviously be increased by proper choosing k, and that the intensity of pump can greatly be decreased in the all-optical switching by means of optimizing k, increasing medium length, and choosing sum-frequency generation.
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.
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.
The authors study analytically and numerically the effect of a periodic perturbation in the index of refraction of a nonlinear optical medium. Using a one-dimensional model for monochromatic waves incident on the medium, they find that near resonance between the perturbation and the modulation of the electric field there can be a significant enhancement of optical bistability in the low intensity regime. In particular, they discuss in detail the case of the primary resonance, which is responsible for the most significant effects, and show how one can optimize the bistability curve for the implementation of an optical switch, based on the information provided by the resonance structure.
The scope of this paper is to revisit the use of quadratic crystals cut for second harmonic generation (SHG) with type II phase-matching in view of all-optical processing of light signal. The investigations on this topic mainly focused in the past years on the possibilities opened by cascading of quadratic nonlinearities in phase-mismatched conditions [1]. The goal of this paper is to remind the reader that various types of optical processing are achievable with sum and difference frequency generation in phase-matched position without the requirement for cascaded nonlinearities. In a first part we will report few examples of the use of difference frequency generation (or down conversion) for signal processing. In a second part we will show that type II SHG with unbalanced fundamental inputs may lead to coherent amplification or transistor like operation.
The interaction of coherent light with a nonlinear medium is modeled here by a general quantum anharmonic oscillator. The model is not exactly solvable in a closed analytical form. But we need operator solutions of the equations of motion corresponding to these models in order to study the quantum fluctuations of coherent light in nonlinear media. In the present work we derive approximate operator solutions. From these solutions we observe that there exists an apparent discrepancy between the solutions obtained by different techniques. We compare different solutions and conclude that all correct solutions are equivalent and the apparent discrepancy is due to the use of different ordering of the operators. We use these solutions to investigate the possibilities of observing different optical phenomena in a nonlinear dielectric medium. To be precise, we have studied quantum phase fluctuations of coherent light in a third order inversion symmetric nonlinear medium. Fluctuations in phase space quadrature for the same system are studied and the possibility of generating squeezed state is reported. Fluctuations in photon number are studied and the nonclassical phenomenon of antibunching is predicted. We have generalized the results obtained for third order nonlinear medium and have studied the interaction of an intense laser beam with a general (m-1)-th order nonlinear medium. Aharanov Anandan nonadiabatic geometric phase is also discussed in the context of (m-1)-th order nonlinear medium.
The problem with generating of new frequencies (signal and idler waves) in parametric four-photon processes without including the Raman scatter was solved only in approximation for a constant electric field or a constant intensity of the pump wave. The overall task which includes the change in intensity and the phase of the pump wave has not been studied in detail in the literature up to now. The main idea of present work is to solve the more general problem in which we have energy exchange between pump wave, signal and idler waves.