  The LUXE experiment is designed to explore the strong-field QED regime in
interactions of high-energy electrons from the European XFEL in a powerful
laser field. One of the crucial aims of this experiment is to measure the
production of electron-positron pairs as a function of the laser field strength
where non-perturbative effects are expected to kick in above the Schwinger
limit. For the measurements of positron energy and multiplicity spectra, a
tracker and an electromagnetic calorimeter are foreseen. The expected number of
positrons varies over ten orders of magnitude and has to be measured over a
widely spread low-energy background. To overcome these challenges, a compact
and finely segmented calorimeter is proposed. The concept of a sandwich
calorimeter made of tungsten absorber plates interspersed with thin sensor
planes is developed. The sensor planes comprise a silicon pad sensor, flexible
Kapton printed circuit planes for bias voltage supply and signal transport to
the sensor edge, all embedded in a carbon fiber support. The thickness of a
sensor plane is less than 1 mm. A dedicated readout is developed comprising
front-end ASICs in 130 nm technology and FPGAs to orchestrate the ASICs and
perform data pre-processing. As an alternative, GaAs are considered with
integrated readout strips on the sensor. Prototypes of both sensor planes are
studied in an electron beam of 5 GeV. Results will be presented on the
homogeneity of the response and edge effects.
