and the efficiency of this device decays rapidly as the order of harmonic increases we now describe a lateral field nth harmonic resonator which has an effective coupling constant much larger than k 2 o n 2 fig7 shows a set of lateral field electrodes 70 70 39 of length 1 separated by a gap of length g disposed on a piezoelectric crystal 73 having thickness t p which is n acoustic half wavelengths the electrical capacity of the lateral field electrodes can be calculated precisely but for this discussion we assume that the capacity of the electrodes is equivalent to the capacity of the imaginary parallel plate structure 74 74 39 shown in phantom in fig7 where the length of the imaginary plates is shown as dimension d in this structure equ4 the uniform lateral electric field of this equivalent capacitor is assumed to be approximately equal to the lateral electric field of the original electrodes the electric field is also assumed to be uniform over d t p n acoustic half waves and the effective coupling constant is equ5 where k o 2 is the coupling constant of the piezoelectric material for fundamental mode lateral field excitation for 1 lt t p the effective coupling constant becomes equ6 writing tp as n 2 where is the acoustic wavelength of the nth harmonic wave and choosing g 1 u221a 3 4 the effective coupling constant for the nth harmonic becomes equ7 that the coupling of the nth harmonic can be made as large as that of the fundamental is a consequence of the electric field flux distribution of small gap lateral field electrodes this phenomenon is illustrated in fig8 a and 8b structure 80 of fig8 a represents a resonator.