Paper detail

Far Field measurement in the focal plane of a lens : a cautionary note

We study theoretically the accuracy of the method based on the Fourier property of lenses that is commonly used for the far field measurement. We consider a simple optical setup in which the far-field intensity pattern of a light beam passing through a Kerr medium is recorded by a CCD camera located in the back focal plane of a thin lens. Using Fresnel diffraction formula and numerical computations, we investigate the influence of a slight longitudinal mispositioning of the CCD camera. Considering a coherent gaussian beam, we show that a tiny error in the position of the CCD camera can produce a narrowing of the transverse pattern instead of the anticipated and well-understood broadening. This phenomenon is robust enough to persist for incoherent beams strongly modified by the presence of noise. The existence of this phenomenon has important consequences for the design and the realization of experiments in the field of optical wave turbulence in which equilibrium spectra reached by incoherent waves can only be determined from a careful far-field analysis. In particular, the unexpected narrowing of the far field may be mistaken for the remarkable phenomenon of classical condensation of waves. Finally, we show that the finite-size of optical components used in experiments produces diffraction patterns having wings decaying in a way comparable to the Rayleigh-Jeans distribution reached by incoherent wave systems at thermodynamical equilibrium.