In this paper, we explore theoretically and experimentally the laser beam shaping ability resulting from the coaxial superposition of two coherent Gaussian beams (GBs). This technique is classified under interferometric laser beam shaping techniques contrasting with the usual ones based on diffraction. The experimental setup does not involve the use of some two-wave interferometer but uses a spatial light modulator for the generation of the necessary interference term. This allows one to avoid the thermal drift occurring in interferometers and gives a total flexibility of the key parameter setting the beam transformation. In particular, we demonstrate the reshaping of a GB into a bottle beam or top-hat beam in the focal plane of a focusing lens.
The cosine Gaussian beam (CGB) resulting from the coherent coaxial superposition of two Gaussian beams having the same width W and opposite radii of curvature R and − R is a ringed beam characterized by an M2 factor which can be very high, and adjustable by changing R. According to the paper by Hasnaoui et al(2011 Opt. Commun.284 1331–4) we expect that the CGB after ‘rectification’ by a binary diffractive optical element could be a good candidate for focal volume reduction, so useful to many laser applications. Unfortunately, this is not the case, and the physical factors responsible for this unexpected behaviour have been analysed. In particular, we have demonstrated that the three features (M2 factor, divergence and on-axis intensity) do not hold the same information about the spatial characteristics of rectified or unrectified CGBs.
We consider the transformation of a Gaussian laser beam into a flat-top intensity profile or into an optical bottle beam (OBB) by resorting to a diffractive or an interferometric method. The diffractive technique is based on the use of a diffractive optical element consisting in a π-plate, while the interferometric technique uses a Michelson interferometer (MI). The coaxial superposition of two coherent Gaussian beams yields to a flat-top or a OBB in the focal plane of a lens depending on the geometric characteristics of the MI. The performances of the two techniques are compared.
The modelling of the Gaussian beam propagation through an inhomogeneous medium can be viewed as a distributed lensing effect (DLE). The latter takes the form of a Kerr lens effect characterised by a transverse phase profile, which is Gaussian in shape. It is convenient to characterise the DLE by an effective focal length, for which the value depends upon the modelling used. We compare four possible formulations of the effective focal length characterising a Kerr DLE.
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