Simultaneous unidirectional reciprocal filters of electromagnetic and elastic waves based on the modal symmetry of phoxonic crystal waveguides and cavity

Highlights

• Simultaneous unidirectional filter of photons and phonons is achieved.

• A single phoxonic crystal is used to realize unidirectional reciprocal transmission by breaking the spatial-reversal symmetry.

• Elastic wave propagated in the solid material is considered for possible applications in enhancing acousto-optic coupling.

Abstract

We theoretically achieve the simultaneous unidirectional reciprocal filter of electromagnetic (EM) and elastic waves in a single phoxonic crystal by the finite-element method. The functionality is achieved by matching and mismatching the modal symmetry between a resonant cavity and two mutually perpendicular waveguides. Suitable phoxonic cavity and waveguides are created to realize the match and mismatch of the modal symmetry for both EM and elastic waves. The proposed device has the abilities of phoxonic unidirectional filtering as well as providing great potential for enhancing acousto-optic coupling by simultaneously tailoring electromagnetic and elastic waves with an ultracompact footprint size.

Introduction

In recent years, the abilities of guiding, controlling and confining electromagnetic (EM) and elastic waves simultaneously have attracted much attention in periodic or quasiperiodic structures. These structures are termed as phoxonic crystals (PhXCs) [1], [2], [3], optomechanical crystals [4], [5], or phoxonic quasicrystals [6], [7], [8], which possess the phoxonic bandgaps (the coexistence of photonic and phononic bandgaps) [1], [6]. PhXCs provide the possibility to achieve compact on-chip solutions for various dual optical and acoustic applications. Such integrated platform has been used to realize enhancing acoustic-optical interaction [9], [10], [11], [12], [13], [14] and opto-mechanical [5], [10], [14] on a wavelength scale, phoxonic sensing [15], phoxonic cavities [16] and filters [17].

It is indispensable to develop unidirectional routing networks to realize the independent operation of optical and acoustic signals on an integrated platform. Thus unidirectional transmission components are important in optical or acoustic circuits since they can offer unidirectional propagation of optical or acoustic signals [18], [19], [20], [21]. Considerable efforts have been dedicated to independently investigate the unidirectional transmission of the light or sound. Unidirectional propagation can be achieved by breaking the time-reversal symmetry based on the magneto-optical effect for light [22], [23], [24], using macroscopic flow field for sound [25], [26], and using nonlinear effect for both light and sound [27], [28], [29], [30], [31], [32]. Alternatively, unidirectional optical or acoustic propagation has also been intensively realized by breaking the spatial-inversion symmetry with the use of the artificial structures with reciprocal materials, such as gratings [33], metasurfaces [34], and photonic or phononic crystals [35], [36], [37], [38], [39], [40]. In addition, the unidirectional transmission of elastic waves has also been realized in solid/solid phononic crystal [41], [42]. The size of those devices can be remarkably reduced since this kind of structures avoids the use of external sources (e.g. magnetic field or high-intensity sources).

The coexistence of photonic and phononic unidirectional transmission in PhXCs allows for the potential route to realize integrated management of light and sound, highly controllable photon-phonon interactions with an ultracompact footprint size, thus the concept of phoxonic unidirectional transmission was recently proposed and investigated based on hybrid structures of grating-phoxonic crystals by combining diffraction and bandgap effects [43]. The undirectional transmission proposed by Chen et al. is based on the phoxonic structures of solid rods in air, meaning that the acoustic wave is propagated in the air [43]. Acousto-optic effect stems from the elastic strain caused by the elastic wave passing through the medium [9], [13]. However, the elastic strain of acoustic wave in air is rather weak, making that the acousto-optic effect in the air will be barely noticeable. Thus those structures are not suitable for enhancing acousto-optic effect. In this letter, we achieve the dual unidirectional propagation of EM and elastic waves using a single configuration of solid/solid PhXC, which involves a relatively simpler technological process for actual fabrication compared with the composite structures. Furthermore, the proposed phoxonic structure of solid rods in solid ensures that the elastic wave is propagated in the solid, enabling that the acousto-optic effect can be possibly enhanced. The functionality is achieved by matching and mismatching modal symmetry between resonant cavity and waveguides. Although this mechanism has been used to independently achieve unidirectional filters for photons in photonic crystal [35] and phonons in phononic crystals [37], [39], the coexistence of unidirectional propagation for EM and elastic waves doesn't be easily obtained due to the different characteristics of photonic and phononic modes in a same structure. The unidirectional transmission is essentially reciprocal due to the passive and linear structure. Such an unidirectional filter allows a new potential possibility to realize integrated management of photons and phonons, and enhance photon-phonon interactions with an ultracompact footprint size.