Laterally coupled bulk acoustic wave filter comprising, - a vibration layer for carrying bulk acoustic waves, - electrode means comprising a first electrode coupled to the vibration layer for exciting in the vibration layer at least one longitudinal wave mode having a first frequency band and one shear wave mode having a second frequency band, and a second electrode coupled to the vibration layer for sensing a filter pass signal, the first and second electrodes being laterally arranged with respect to each other, - an acoustic reflector structure in acoustic connection with the vibration layer , wherein - the acoustic reflector structure is adapted to acoustically isolate the vibration layer from its surroundings at the first frequency band more efficiently than at the second frequency band for suppressing the effect of the shear wave mode at the second frequency band from the filter pass signal, - the reflector structure comprises a stack of at least four alternatingly ordered high and low acoustic impedance layers (75a-e), the intrinsic acoustic impedance of each of the low-impedance layers being not more than that of any of the high-impedance layers . - the thickness of the topmost layer of the stack closest to the vibration layer is larger than the layer thickness of a corresponding layer in an ideal acoustic Bragg reflector for the longitudinal wave mode, whose reflectance is at its highest for the second frequency band, - the thickness of at least one of the layers (75b-e) of the stack below the topmost layer is smaller than the layer thickness of a corresponding layer in the ideal acoustic Bragg reflector for the longitudinal wave mode, whose reflectance is at its highest for the second frequency band. - a vibration layer for carrying bulk acoustic waves, - electrode means comprising a first electrode coupled to the vibration layer for exciting in the vibration layer at least one longitudinal wave mode having a first frequency band and one shear wave mode having a second frequency band, and a second electrode coupled to the vibration layer for sensing a filter pass signal, the first and second electrodes being laterally arranged with respect to each other, - an acoustic reflector structure in acoustic connection with the vibration layer , - the acoustic reflector structure is adapted to acoustically isolate the vibration layer from its surroundings at the first frequency band more efficiently than at the second frequency band for suppressing the effect of the shear wave mode at the second frequency band from the filter pass signal, - the reflector structure comprises a stack of at least four alternatingly ordered high and low acoustic impedance layers (75a-e), the intrinsic acoustic impedance of each of the low-impedance layers being not more than that of any of the high-impedance layers . - the thickness of the topmost layer of the stack closest to the vibration layer is larger than the layer thickness of a corresponding layer in an ideal acoustic Bragg reflector for the longitudinal wave mode, whose reflectance is at its highest for the second frequency band, - the thickness of at least one of the layers (75b-e) of the stack below the topmost layer is smaller than the layer thickness of a corresponding layer in the ideal acoustic Bragg reflector for the longitudinal wave mode, whose reflectance is at its highest for the second frequency band. <EOS>