Innovative Phase Plates for Beam Shaping

In light optics the use of holographic beam shaping has been largely used to obtain complicated
wavefronts [1] and vortex beams but recently holograms have been used in the electron vortex beam
generation [2]. We show here our recent improvement in the technology of hologram fabrication by
means of “phase hologram” [3] replacing the amplitude hologram so far used. Phase hologram
appropriately changes the phase of the wavefront by a modulation of thickness in a Silicon nitride thin
membrane.
By means of phase hologram we could produce different beam shape in both Fresnel and Fraunhofer
regime. Moreover we engineered the hologram shape to obtain high efficiency on the generated
wavefunction. Presently we could demonstrate an efficiency of 40% in the generation efficiency for a
single beam. This is the best performance ever shown and is much higher than amplitude hologram so
far used.
The particular holographic technique consists in creating a grating of Si3N4 and modulating the
periodicity with the desired wavefront shape. In general many order of diffraction of the grating are
generated while only the first order is typically interesting for application with a clear loss of intensity.
However if the groove of the grating is a ramp spanning an appropriate thickness corresponding
exactly to 2π phase in the electron path (also dubbed “blazed” profile) a single diffraction with the
relevant beam can be obtained.
Using this principle we generated by FIB a close to ideal hologram. The experimental thickness
profile (as calculated by EELS) is shown in fig 1a. In the inset a profile in a line is extracted and
compared with the “ideal” blazed pattern.
The full pattern for the generation of a Bessel beam is shown in fig 1b while the resulting series of
beam in a Fresnel plane is shown in fig 1c. In particular the experimental pattern (up) is compared with
the simulated one based Fresnel integral of the hologram in fig 1a [3]. The very good agreement means
that the simulated phase is also correct. Therefore the figure in the inset that represents intensity and
phase of the simulated beam can be considered as a realistic representation of the actual phase.