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Register a new userControl of spatial four wave mixing efficiency in Bessel beams using longitudinal intensity shaping
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Added by
Francois Courvoisier
Publication date
2019
fields
Physics
and research's language is
English
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Diffraction-free Bessel beams have attracted major interest because of their stability even in regimes of nonlinear propagation and filamentation. However, Kerr nonlinear couplings are known to induce significant longitudinal intensity modulation, detrimental to the generation of uniform plasma or for applications in the processing of transparent materials. These nonlinear instabilities arise from the generation of new spatio-spectral components through an initial stage of continuous spectral broadening followed by four wave mixing. In this paper, we investigate analytically and numerically these processes and show that nonlinear instabilities can be controlled through shaping the spatial spectral phase of the input beam. This opens new routes for suppressing the nonlinear growth of new frequencies and controlling ultrashort pulse propagation in dielectrics.
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Several applications, such as optical tweezers and atom guiding, benefit from techniques that allow the engineering of optical fields spatial profiles, in particular their longitudinal intensity patterns. In cylindrical coordinates, methods such as Frozen Waves allow an advanced control of beams characteristics, but in Cartesian coordinates there is no analogous technique. Since Cartesian beams may also be useful for applications, we develop here a method to modulate on-demand the longitudinal intensity pattern of any (initially) unidimensional Cartesian beam with concentrated wavevector spectrum, thus encompassing all paraxial unidimensional beams. To this end, we write the total beam as a product of two unidimensional beams and explore the degree of freedom provided by the additional Cartesian coordinate. While in the plane where this coordinate is zero the chosen unidimensional beam keeps its structure with the additional desired intensity modulation, a sinusoidal-like oscillation appears in the direction of this variable and creates a spot whose size is tunable. Examples with Gaussian and Airy beams are presented and their corresponding experimental demonstrations are performed to show the validity of the method.
Cylindrical vector (CV) beams are a set of transverse spatial modes that exhibit a cylindrically symmetric intensity profile and a variable polarization about the beam axis. They are composed of a non-separable superposition of orbital and spin angular momentum. Critically, CV beams are also the eigenmodes of optical fiber and, as such, are of wide-spread practical importance in photonics and have the potential to increase communications bandwidth through spatial multiplexing. Here, we derive the coupled amplitude equations that describe the four-wave mixing (FWM) of CV beams in optical fibers. These equations allow us to determine the selection rules that govern the interconversion of CV modes in FWM processes. With these selection rules, we show that FWM conserves the total angular momentum, the sum of orbital and spin angular momentum, in the conversion of two input photons to two output photons. When applied to spontaneous four-wave mixing, the selection rules show that photon pairs can be generated in CV modes directly and can be entangled in those modes. Such quantum states of light in CV modes could benefit technologies such as quantum key distribution with satellites.
The dynamical degenerate four-wave mixing is studied analytically in detail. By removing the unessential freedom, we first characterize this system by a lower-dimensional closed subsystem of a deformed Maxwell-Bloch type, involving only three physical variables: the intensity pattern, the dynamical grating amplitude, the relative net gain. We then classify by the Painleve test all the cases when singlevalued solutions may exist, according to the two essential parameters of the system: the real relaxation time tau, the complex response constant gamma. In addition to the stationary case, the only two integrable cases occur for a purely nonlocal response (Real(gamma)=0), these are the complex unpumped Maxwell-Bloch system and another one, which is explicitly integrated with elliptic functions. For a generic response (Re(gamma) not=0), we display strong similarities with the cubic complex Ginzburg-Landau equation.
A common issue encountered in photoemission electron sources used in electron accelerators is the transverse inhomogeneity of the laser distribution resulting from the laser-amplification process and often use of frequency up conversion in nonlinear crystals. A inhomogeneous laser distribution on the photocathode produces charged beams with lower beam quality. In this paper, we explore the possible use of microlens arrays (fly-eye light condensers) to dramatically improve the transverse uniformity of the drive laser pulse on UV photocathodes. We also demonstrate the use of such microlens arrays to generate transversely-modulated electron beams and present a possible application to diagnose the properties of a magnetized beam.
Bessel beams are plane waves with amplitude profiles described by Bessel functions. They are important because of their property of limited diffraction and their capacity to carry orbital angular momentum. Here we report the creation of a Bessel beam of de Broglie matter waves. The Bessel beam is produced by the free evolution of a thin toroidal atomic Bose-Einstein condensate (BEC) which has been set into rotational motion. By attempting to stir it at different rotation rates, we show that the toroidal BEC can only be made to rotate at discrete, equally-spaced frequencies, demonstrating that circulation is quantized in atomic BECs. The method used here to generate matter wave Bessel beams with a Painted Potential can be viewed as a form of wavefunction engineering which might be extended to implement arbitrary cold atom matter wave holography.
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