通过并行因子分解模拟极高模式数下的多模非线性效应

中文摘要 AI 辅助

非线性光学前沿的多种问题涉及强多模相互作用。由于评估大量非线性重叠的复杂性，模拟这些动力学通常在计算上具有挑战性。这在超快克尔效应物理中尤为突出，其中模态表示下的模拟具有随模式数四次方缩放的一般复杂度。这限制了实践中模拟中可保留的最大模式数仅为几十个（通常更少），即使在现代GPU上运行也是如此。在此，我展示了如何利用非线性重叠张量的并行因子分解，可以容纳远更多的模式。对于没有特殊对称性或可分离性的通用折射率分布，实际值可达数千，而具有特殊对称性时，则可远大于此。我证明了在现代硬件上可以进行包含超过1000个模式的模拟，并以多模孤子在梯度折射率光纤中传播一米为例进行了说明。我进一步表明，改进的缩放使得考虑统计效应立即变得可行，并以孤子裂变中的噪声放大为例进行了说明。这些结果已在公开代码中实现并附有示例，应能支持模拟多模非线性光学中最严苛的机制。非线性相互作用张量的压缩可能为更高效地模拟各种其他系统中的非线性波动力学提供途径，包括声学、水波、声子学、磁子学和玻色凝聚体。

英文摘要

A variety of problems at the frontier of nonlinear optics involve strongly multimode interactions. Simulating these dynamics is often computationally challenging due to the complexity of evaluating a large number of nonlinear overlaps. This is especially acute in ultrafast Kerr effect physics, where simulations in a modal representation have a generic complexity scaling quartically with the number of modes. This has limited the largest number of modes retainable in simulations in practice to a few tens of modes (often fewer), even when run on modern GPUs. Here, I show how by taking advantage of parallel factor decompositions of the nonlinear overlap tensor, a far larger number of modes can be accommodated. Realistic values for generic index profiles without special symmetries or separability can be in the thousands, and with special symmetries, far larger. I show that simulations with $>$1,000 modes can be done on modern hardware, illustrating this with the example of a multimode soliton propagating over a meter of GRIN fiber. I further show that the improved scaling immediately makes it practical to consider statistical effects, illustrating with the example of noise amplification in soliton fission. These results, implemented in public code with examples, should enable access to simulating the most demanding regimes of multimode nonlinear optics. Compression of the nonlinear interaction tensor may provide a route for more efficient simulation of nonlinear wave dynamics across a variety of other systems including acoustics, water waves, phononics, magnonics, and Bose condensates.

发表机构

• School of Applied and Engineering Physics, Cornell University（康奈尔大学应用工程物理学院）

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