弯曲波导耦合器中作为反绝热生成元的横向动量

中文摘要 AI 辅助

弯曲模式演化耦合器的轴会抑制其超模之间的非绝热耦合，此类弯曲耦合器最近被证明可实现反绝热（CD）协议。在此，我们确定了负责该协议的算符。波导结构的刚性横向位移由横向动量 $\hat p_x$ 生成，其在实数超模基中的对角矩阵元为零，非对角元为纯虚数；在双模系统中，这样的算符正比于 $\sy$。双波导耦合器的CD项本身正比于 $\sy$，而失谐和耦合这两个由波导宽度和间距设定的参数位于 $\sigma_z$–$\sigma_x$ 平面内，无法产生该项。因此，横向动量是弯曲耦合器的CD生成元，这是必然而非设计使然。将其提供的项与非绝热耦合相等，可得到轴斜率的闭式表达式，即未扰动超模在单个横截面上的两个矩阵元之比，通过对易子恒等式可将其改写为耦合模变量形式：$\dot{\xo}=\dot\theta/(\gamma\dbeta^{2})$。该表达式与数值偏移搜索的结果在0.3%的误差范围内一致，且无需搜索。光束传播模拟验证了该设计，并首次将其与基于相同参考结构构建的直耦合器中通过幺正变换实现的CD协议进行了比较。两种器件分别达到0.994和1.000的超模保真度，而未处理的耦合器仅为0.886，两者在带宽和制造容差上一致，而其内部轨迹的差异恰好等于联系它们的坐标系变换。

英文摘要

Bending the axis of a mode-evolution coupler suppresses the nonadiabatic coupling between its supermodes, and bent couplers of this kind were recently shown to realize the counter-diabatic (CD) protocol. Here we identify the operator responsible. Rigid lateral displacement of a waveguide structure is generated by the transverse momentum $\hat p_x$, whose diagonal matrix elements vanish in a real supermode basis and whose off-diagonal element is purely imaginary; in a two-mode system such an operator is proportional to $\sy$. The CD term of a two-waveguide coupler is itself proportional to $\sy$, while the detuning and the coupling, the two parameters set by the waveguide widths and spacing, lie in the $σ_z$--$σ_x$ plane and cannot produce it. The transverse momentum is therefore the CD generator of the bent coupler, by necessity rather than by design. Equating the term it supplies to the nonadiabatic coupling gives the axis slope in closed form as a ratio of two matrix elements of the unperturbed supermodes at a single cross section, which a commutator identity recasts in coupled-mode variables as $\dot{\xo}=\dotθ/(γ\dbeta^{2})$. The expression agrees with the numerical offset search to $0.3\%$ and requires no search. Beam propagation simulations confirm the design and compare it, for the first time, with the CD protocol realized by unitary transformation in a straight coupler built from the same reference structure. The two devices reach $0.994$ and $1.000$ supermode fidelity where the untreated coupler reaches $0.886$, and agree in bandwidth and fabrication tolerance, while their internal trajectories differ by exactly the frame transformation that relates them.

发表机构

• National Cheng Kung University（国立成功大学）

机构由 AI 辅助整理，请以论文原文为准。