We present a novel approach for designing non-uniform binary long-period gratings with predefined transmission characteristics by directly optimizing the coupling strengths and lengths of the constituent waveguides in all grating segments. The optimal grating parameters were determined by minimizing the deviation of the transmission characteristics calculated using the transfer matrix method from the predefined target functions using the multistart optimization procedure. We demonstrate the effectiveness of the proposed method by optimizing the performance of grating-based TE ₀ /TE ₁ mode converters in a few-mode buried waveguide composed of medium-contrast materials (TiO ₂ :SiO ₂ /SiO ₂ ). Two converters with coupling caused by the lateral shift and step-like thickness change of adjacent waveguides were numerically optimized for the 1.3 and 1.55 μm bands. Each of the optimized devices has a total length of approximately 250 μm. For both types of converters, a spectral range of 150 nm with crosstalk lower than −20 dB was obtained for the two communication windows using at most nine grating segments, with twice lower excess loss for the grating with a step-like thickness change. Moreover, for such grating composed of only 9 segments it is possible to obtain the conversion band of 400 nm, covering both communication windows with an excess loss lower than 0.45 dB and crosstalk below −20 dB. We also numerically analyzed the impact of the fabrication tolerances on the converter characteristics.

中文翻译：

---

基于非均匀二值长周期光栅的宽带集成模式转换器的直接多参数优化设计

我们提出了一种新颖的方法，通过直接优化所有光栅段中组成波导的耦合强度和长度来设计具有预定义传输特性的非均匀二元长周期光栅。通过使用多起点优化程序最小化使用传输矩阵方法计算的传输特性与预定义目标函数的偏差来确定最佳光栅参数。我们通过优化由中等对比度材料（TiO ₂ :SiO ₂ /SiO ₂ ）组成的少模埋置波导中基于 光栅的TE ₀ /TE ₁模式转换器的性能来证明该方法的有效性 。针对 1.3 和 1.55 μm 频段对由相邻波导的横向位移和阶梯式厚度变化引起耦合的两个转换器进行了数值优化。每个优化器件的总长度约为 250 μm。对于两种类型的转换器，使用最多九个光栅段的两个通信窗口获得了 150 nm 的光谱范围，串扰低于 -20 dB，并且具有阶梯状厚度变化的光栅的额外损耗降低了一倍。此外，对于这种仅由9段组成的光栅，可以获得400 nm的转换频带，覆盖两个通信窗口，超额损耗低于0.45 dB，串扰低于-20 dB。我们还数值分析了制造公差对转换器特性的影响。