Non-reciprocal frequency conversion in a two-dimensional waveguide incorporating a local nonlinear gate

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We study non-reciprocal frequency conversion in a linear two-dimensional (2D) acoustic waveguide consisting of coupled oscillators incorporating a local asymmetric gate of nonlinearly coupled oscillators. The 2D waveguide supports an acoustic and an optical frequency band. We consider a monochromatic harmonic excitation at the acoustic band that initiates a propagating wave in the linear waveguide. As the wave scatters across the nonlinear gate, its frequency is converted to a higher (triple) harmonic in the optical band. This frequency conversion is due to a local 1:3 internal resonance at the nonlinear gate. The efficacy and robustness of the frequency conversion are validated by direct numerical simulations. A large portion of the energy of the wave is transmitted across the nonlinear gate with converted frequency and this frequency conversion is realized robustly over a range of excitation frequencies and magnitudes. In addition, owing to the nonlinearity, the frequency conversion is tunable to frequency and energy. The transmissibility (i.e., transmitted over reflected energy at the gate) is sensitive to the excitation parameters indicative of bifurcations of the nonlinear acoustics. Lastly, frequency conversion induces strong non-reciprocity in the acoustics since the energy transfer with frequency conversion is only realizable in a preferred direction of wave propagation and prohibited in the reverse direction. The methodology and results of the present nonlinear frequency converter are applicable to various fields including targeted energy transfer in phononic systems and acoustic computing.

Original languageEnglish (US)
Article number107041
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - Apr 2023


  • Acoustic non-reciprocity
  • Frequency conversion
  • Internal resonance
  • Waveguide

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics


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