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We report on highly efficient four-wave optical parametric amplification in a water cell pumped by an elliptically shaped, ultrashort pulsed laser beam under non-collinear phase-matching configuration. Energy conversion from pump to parametric waves as high as 25 % is obtained owing to the achievement of 1-dimensional spatial-soliton regime, which guarantees high intensity over a large interaction length and ensures high beam quality.

Efficient broadband four-wave optical parametric amplification in bulk Kerr medium (fused silica) is demonstrated by means of noncollinear phase matching and cylindrical focusing geometry without the onset of beam breakup and filamentation. Amplified signal energy as high as 180 microJ with 1 ps, 1.8 mJ pumping at 1,055 nm is achieved with pump-to-signal energy conversion close to 10%. More than 70 nm FWHM parametric gain bandwidth around 740 nm is demonstrated without imposing angular dispersion on the frequency components of the broadband seed signal.

In contradistinction to a widespread belief that the spatial localization of photons is restricted by a power-law falloff of the photon energy density, I.Bialynicki-Birula [Phys. Rev. Lett. 80, 5247 (1998)] has proved that any stronger -up to an almost exponential -falloff is allowed. We are showing that for certain specifically designed cylindrical one-photon states the localization is even better in lateral directions. If the photon state is built from the so-called focus wave mode, the falloff in the waist cross-section plane turns out to be quadratically exponential (Gaussian) and such strong localization persists in the course of propagation.While quantum electrodynamics (QED) underwent an impressive development and reached its maturity in the middle of the last century, one of its basic conceptsthe photon wave function in free space -was deprived of such fortune. Although the photon wave function in coordinate representation was introduced already in 1930 by Landau and Peierls [1] the concept was found to suffer from inherent difficulties that were not overcome during the century (see review [2]). The common explanation presented in textbooks (e.g., [3], [4]) may be summed up as follows: (i) no position operator exists for the photon, (ii) while the position wave function may be localized near a space-time point, the measurable quantities like the electromagnetic field vectors, energy, and the photodetection probability remain spread out due to their non-local relation with the position wave function. However, just before the turn of the century both of these widely-espoused notions were disproved [5], [6] and in the new century a fresh interest in the photon localization problem seems to have been awakened (see, e.g., [7],[8], [9]), meeting the needs of developments in near-field optics, cavity QED, and quantum computing.I. Bialynicki-Birula writes [6] that the statement "even when the position wave function is strongly concentrated near the origin, the energy wave function is spread out over space asymptotically like r −7/2 " (citation from [4], p. 638) is incorrect and that both wave functions may be strongly concentrated near the origin. He demonstrates, on one hand, that photons can be essentially better localized in space -with an exponential falloff of the photon energy density and the photodetection rates. On the other hand, he establishes -and it is even somewhat startling that nobody has done it earlier -that certain localization restrictions arise out of a mathematical property of the positive frequency solutions which therefore are of a universal character and apply not only to photon states but hold for all particles. More specifically, it has been proven in the Letter [6] for the case of spherically imploding-exploding one-photon wavepacket that the Paley-Wiener theorem allows even at instants of maximal localization only such asymptotic decrease of the modulus of the wave function with the radial distance r that is slower than the linear exponential one, i.e., anything slower than ∼...

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