Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials

Abstract

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports.T he pursuit of novel devices that are able to manipulate energy, mass and information transmission has stimulated huge interests in widespread physical branches such as phononics 1 , photonics 2-4 and biophysics 5. As one of the most fundamental and applicable devices, the wave diode can rectify non-reciprocal wave propagation, in analogy to electronic p-n junctions, where the transmission coefficient is significantly directiondependent. As such, the device conducts in the forward direction but insulates in the backward one. There are many interesting theoretical proposals for thermal diodes [6][7][8][9][10] , optical diodes 11,12 , spin Seebeck diodes 13,14 and acoustic diodes 15,16 , and many of them have been successfully verified by experiments [2][3][4][17][18][19][20][21] . It has been well established that linear structures are not able to break the reciprocity in reflection-transmission once the time-reversal symmetry is preserved 22 . Therefore, both nonlinearity and some kinds of symmetry breaking mechanism are essential for the real non-reciprocal propagation. In particular, the optical isolators or diodes 23 have been realized by harvesting the properties of nonlinearity and asymmetry [24][25][26][27][28][29] . The enhancement of nonreciprocal transmission via cascading has also been studied 30 . And this nonreciprocal transmission has even been achieved in PT systems 31,32 . Recently, an interesting design of wave diode is proposed 33 , based on the nonreciprocal transmission in a one-dimensional (1D) nonlinear layer structure 11,12 . The model system is described by the discrete nonlinear Schrödinger (DNLS) equation, which is a reasonable approximation for the wave evolution in layered photonic or phononic crystals 34 . The spatially varying coefficients break the mirror reflection symmetry and this non-homogeneity generates the asymmetric wave propagation together with nonlinearity. However, the inhomogeneity of coefficients is not the only way to achieve non-reciprocal wave propagation and also it is usually very hard to design the inhomogeneous coefficient in real materials.To circu...