The principle of reciprocity underpins one of the fundamental effects in optics which signifies symmetric transmission with respect to the interchange of the source and observation points. Breaking reciprocity, however, would enable additional functionalities and greatly enriches the applications of photonics in terms of novel nonreciprocal devices. Here, a realistic nanoscale cascaded-cavity system that envisages nonreciprocal optical isolation and efficient wavelength conversion based on spatiotemporally modulated index of refraction are proposed and numerically demonstrated. The on-chip, linear, magnetic-free nonreciprocal isolation and dynamically controllable wavelength conversion can be a promising candidate for silicon nanophotonic and opto-electronic devices. {1. Introduction} In classical electromagnetism, the principle of Lorentz reciprocity states that the response of a transmission channel is symmetric when source and observation points are interchanged. It implies the symmetry in Green’s functions, and the identical reception and radiation property of antennas ${}^{[1-3]}$. Breaking Lorentz reciprocity enables optical nanostructures to be used for intriguing functionalities such as optical isolation, which plays significant roles in efficient design of integrated optical systems via laser feedback protection, alleviating multipath interference not achievable in reciprocal structures $^{[4,\thinspace 5]}$. A couple of distinctive yet conventional approaches exist toward creating nonreciprocity to achieve optical isolation. Applying an external magnetic field, which can lead to the asymmetric permittivity tensor of magneto-optical materials, is the most common way to break the reciprocity between forward and backward propagating modes ${}^{[6-11]}$. However, magneto-optical materials are typically very lossy at optical frequencies, and it is challenging to integrate them on chip-scale devices with low cost and in a CMOS compatible manner. Recently, due to the great demand for nonreciprocal photon transport in miniaturized and chip-compatible systems, alternative strategies for non-magnetic optical isolation have been proposed. For instance, using optical nonlinearity, Lorentz reciprocity could be broken due to the dependence of the dielectric function on the electric field strength, but these are typically limited to specific operating conditions and strong input signals ${}^{[5]}$. In addition, we can achieve nonreciprocity by biasing with other quantities that break time-reversal symmetry, including direct electric current $^{[12,\thinspace 13]}$. More recently, the dynamic temporal modulation of refractive index has been widely explored to break the Lorentz reciprocity ${}^{[13-19]}$, which promises a new route towards magnetic-free and on-chip nonreciprocal components, like optical isolators and circulators. This dynamic time modulation can be incorporated in several ways, imparting a synthetic linear or angular momentum to a structure without moving its constituting parts. As a typical example, in a spatiotemporally-modulated waveguide ${}^{[14]}$, a shift of energy and momentum can be provided by the space-time modulation to enable a transition between two photonic modes propagating along one direction. However, no transition occurs in the …

中文翻译：

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通过时空工程级联腔进行不可逆的隔离和波长转换

互惠原理是光学的基本作用之一，它表示相对于源和观测点互换的对称传输。然而，打破互惠性将使附加功能性得以实现，并且就新颖的不可逆设备而言，极大地丰富了光子学的应用。在这里，提出了一种现实的纳米级联腔系统，该系统设想了不可逆的光学隔离和基于时空调制折射率的有效波长转换。片上线性无磁不可逆隔离和动态可控的波长转换可以成为硅纳米光子和光电器件的有希望的候选者。{1。简介}在古典电磁学中，洛伦兹互惠原理指出，当交换源点和观察点时，传输通道的响应是对称的。它暗示了格林函数的对称性，以及天线的相同接收和辐射特性${}^{[\mathrm{1个}-3]}$。突破性的洛伦兹互惠性使光学纳米结构可用于吸引人的功能，例如光学隔离，通过激光反馈保护在集成光学系统的高效设计中发挥重要作用，从而减轻了互易结构中无法实现的多径干扰$ ^ {[4，\ thinspace 5 ]} $。存在两种独特但常规的方法来实现不可逆性以实现光学隔离。施加外部磁场可能会导致磁光材料的介电常数张量不对称，这是打破正向和反向传播模式之间互易性的最常见方法${}^{[6-11]}$。但是，磁光材料通常在光频率上损耗很大，以低成本和CMOS兼容的方式将它们集成到芯片级设备上是一个挑战。近来，由于在微型且芯片兼容的系统中对不可逆光子传输的巨大需求，已提出了用于非磁性光学隔离的替代策略。例如，使用光学非线性，由于介电函数对电场强度的依赖性，可能会破坏洛伦兹互易性，但是这些通常限于特定的工作条件和强输入信号${}^{[5]}$。另外，我们可以通过偏置破坏时间反转对称性的其他量（包括直流电流$ ^ {[[12，\ thinspace 13]} $）来实现不可逆性。最近，人们广泛探索了折射率的动态时间调制来打破洛伦兹互易性。${}^{[13-19]}$，这为光隔离器和环行器等无磁性和片上不可逆元件的开发开辟了一条新途径。该动态时间调制可以通过几种方式合并，从而在不移动其组成部分的情况下将合成的线性或角动量赋予结构。作为典型示例，在时空调制波导中${}^{[14]}$可以通过时空调制来提供能量和动量的转移，以实现沿一个方向传播的两个光子模式之间的过渡。但是，在…中没有发生过渡。