Fig. 3. Higher-order acoustic modes.

a. S_yy strain tensor components for three other acoustic modes that can be excited by the transducer. Note that the waveguide location is marked with dashed lines. The frequencies are labeled to be consistent with (f) and (g), but the actual simulated values differ slightly. b A broadband RF drive frequency sweep with incident RF power, P_RF, and optical wavelength, λ, fixed reveals higher order acoustic modes coupling to the optical mode in the spiral with C = 38 modulated segments. c Modulation efficiency for the 706 MHz mode. It is the strongest performing acoustic mode due to the favorable overlap of the S_yy strain tensor component with the waveguide shown in (a). d Theoretical calculations illustrating relative degradation of modulation efficiency as acoustic mode frequency differs from the spiral’s designed frequency. The shaded blue region shows the 3 dB range, indicating all acoustic modes in (a, b) are still expected to nearly satisfy phase-matching considerations. e. Theoretical calculation showing the range of possible modulation index trends expected across the 3 dB shaded region in (d) as a function of modulated segment count. The 706 MHz mode in (f) exhibits behavior similar to the lower dashed black line. f. Scaling of the modulation index for the 706 MHz mode contrasted against the fundamental mode. The provided frequencies are the average of the measured devices, and there is slight variation from device to device. The agreement between the theory and the data validates the behavior claimed in (d). g Modulation index scaling of the 502 MHz and 639 MHz modes. The modulation index multiplicatively increases, as expected from theory.