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arXiv:1401.3788 · Optics Express

Diffraction manipulation by four-wave mixing

Itay Katzir, Amiram Ron, Ofer Firstenberg

Published Mar 2, 2015• 3 citations
arXivHTMLPDF

Abstract

We suggest a scheme to manipulate paraxial diffraction by utilizing the dependency of a four-wave mixing process on the relative angle between the light fields. A microscopic model for four-wave mixing in a Λ-type level structure is introduced and compared to recent experimental data. We show that images with feature size as low as 10 μm can propagate with very little or even negative diffraction. The mechanism is completely different from that conserving the shape of spatial solitons in nonlinear media, as here diffraction is suppressed for arbitrary spatial profiles. At the same time, the gain inherent to the nonlinear process prevents loss and allows for operating at high optical depths. Our scheme does not rely on atomic motion and is thus applicable to both gaseous and solid media.

DOI
10.1364/oe.23.006379

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We suggest a scheme to manipulate paraxial diffraction by utilizing the dependency of a four-wave mixing process on the relative angle between the light fields. A microscopic model for four-wave mixing in a Λ-type level structure is introduced and compared to recent experimental data. We show that images with feature size as low as 10 μm can propagate with very little or even negative diffraction. The mechanism is completely different from that conserving the shape of spatial solitons in nonlinear media, as here diffraction is suppressed for arbitrary spatial profiles. At the same time, the gain inherent to the nonlinear process prevents loss and allows for operating at high optical depths. Our scheme does not rely on atomic motion and is thus applicable to both gaseous and solid media.
A setup to frequency-convert an arbitrary image encoded in the spatial profile of a probe field onto a signal field using four-wave mixing in a thermal atom vapor is proposed. The atomic motion is exploited to cancel diffraction of both signal and probe fields simultaneously. We show that an incoherent probe field can be used to enhance the transverse momentum bandwidth which can be propagated without diffraction, such that smaller structures with higher spatial resolution can be transmitted. It furthermore compensates linear absorption with nonlinear gain, to improve the four-wave mixing performance since the propagation dynamics of the various field intensities is favorably modified.
The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. FEC has already been exploited to produce a matter-wave `laser' leading to the threshold of a new field of physics: nonlinear atom optics. Recently the first experiment in nonlinear atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schrodinger equation (also called the Gross-Pitaevskii equation), to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves.
The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. BEC has already been exploited to produce a matter-wave 'laser' atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schroedinger equation, to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation, and particle number conservation in four-wave mixing of matter waves.
Summary form only given. We investigate the waveguiding induced in a weak probe propagating in a medium of two-level atoms driven by a copropagating, intense, strongly detuned pump. We show that when the transverse profile of the pump exhibits solitonlike oscillations, similar oscillations can be induced in the transverse profile of the probe. The pump acts as a spatial soliton in the sense that its transverse intensity profile displays oscillating spatial behavior due to the interplay of self-focusing and diffraction. This work suggests that the importance of four-wave mixing in modifying induced waveguiding should be considered in other waveguiding schemes. The potential of phase control in manipulating the properties of propagating laser light in a sophisticated way is emphasized.
The nonlinear signal in a degenerate four-wave mixing experiment as a result of diffraction of a spatially distributed third-order nonlinearity is studied theoretically. The approach has been applied for the case of monochromatic and ultrashort pulses. As a consequence, the degenerate four-wave mixing signal is found to be independent of light-coherence parameters and cannot be explained as a product of diffraction on a dynamic grating. In this model only the fast component of the signal (the coherent artifact) is related directly to third-order nonlinear processes. The main features (the origins, temporal shapes, dependencies of pump intensity, and modulation effects) of the coherent artifact and a slow-decay component are discussed theoretically and experimentally.