  We present a detailed study of two novel methods for shaping the light
optical wavefront by employing a transmissive spatial light modulator (SLM).
Conventionally, optical Airy beams are created by employing SLMs in the
so-called all phase mode. In the first method, a numerically simulated lens
phase distribution is loaded directly onto the SLM, together with the cubic
phase distribution. An Airy beam is generated at the focal plane of the
numerical lens. We provide for the first time a quantitative properties of the
formed Airy beam. We derive the formula for deflection of the intensity maximum
of the so formed Airy beam, which is different to the quadratic deflection
typical of Airy beams. We cross-validate the derived formula by both
simulations and experiment. The second method is based on the fact that a
system consisting of a transmissive SLM sandwiched between two polarisers can
create a transmission function with negative values. This observation alone has
the potential for various other wavefront modulations where the transmission
function requires negative values. As an example for this method, we
demonstrate that a wavefront can be modulated by passing the SLM system with
transmission function with negative values by loading an Airy function
distribution directly onto SLM. Since the Airy function is a real-valued
function but also with negative values, an Airy beam can be generated by direct
transfer of the Airy function distribution onto such an SLM system. In this
way, an Airy beam is generated immediately behind the SLM. As both new methods
do not employ a physical lens, the two setups are more compact than
conventional setups for creating Airy beams. We compare the performance of the
two novel methods and the properties of the created Airy beams.
