Software package for thoretical simulations of nonlinear light propagation in photochemical systems

天空中的云的图案，沙漠中的风雕刻条纹，动物皮肤上的斑点和条纹都是自然界中自发出现的图案的例子。在这些不同的系统中，支配自发模式形成的物理定律惊人地相似。任何不稳定的系统（倾向于变化）都会自发地转变，试图达到最稳定的状态（平衡）。如果系统在向平衡演化的过程中受到两种相反的力量的影响，模式就会出现。我们的研究考察了当一个系统同时经历光学和化学变化时的非线性现象。我们已经发现了一系列丰富多样的非线性现象，包括自陷光束，这些光束在长距离传播时不会变宽。我们已经发现了激光和单独的白色光的自陷光束，并了解到它们的性质是根本不同的。组成激光束的波具有相同的波长并且彼此强烈相关。白色光的情况正好相反，它被认为是不相干的，因为它是由整个波长光谱组成的，并且具有极差的相关性。一旦自陷，激光束就会表现出不同的离散光学模式，就像鼓皮的振动模式或小提琴弦的谐波。然而，自陷白色光束的光学模式波动如此之快，以至于只能观察到整个光束的时间平均或平滑轮廓。应用我们的知识之间的竞争衍射和折射的自陷行为，我们最近已经能够证明自发形成的图案，在大的均匀的白色光束。虽然所有这些研究都是通过实验室实验进行的，但现在必须通过理论研究来完成。该申请要求资助购买软件，使我们能够从理论上模拟和建模这些系统的行为，并以这种方式帮助设计进一步的实验。

The patterns of clouds in the sky, the wind-sculpted striations in the desert sand, the spots and stripes of animal skin are examples of patterns that emerge spontaneously in nature. The physical laws that govern spontaneous pattern formation in these dissimilar systems are strikingly similar. Any system that is unstable (prone to change) will spontaneously transform in an attempt to reach its most stable state (equilibrium). Patterns emerge if during its evolution towards equilibrium, the system is subjected to two opposing forces. Our research examines such nonlinear phenomena when a system simultaneously undergoes optical and chemical changes. We have discovered a richly diverse suite of nonlinear phenomena including self-trapped beams of light, which travel without broadening over unexpectedly long distances. We have found self-trapped beams of both laser and separately, of white light and learnt that their properties are fundamentally different. Waves composing a laser beam possess the same wavelength and are strongly correlated to each other. Exactly the opposite is the case for white light, which is said to be incoherent because it is composed of an entire spectrum of wavelengths and has extremely poor correlation. Once self-trapped, a laser beam exhibits different and discrete optical modes - like the vibrational modes of a drum skin or the harmonics of a violin string. The optical modes of a self-trapped white light beam however fluctuate so rapidly that only a time-averaged or smoothed profile of the entire beam can be observed. By applying our knowledge of the competition between diffraction and refraction in self-trapping behaviour, we have recently been able to demonstrate the spontaneous formation of patterns in large uniform beams of white light. While all of these studies have been conducted through experiments in the laboratory, they must now be completed with theoretical studies. This application requests funding to purchase software that will enable us to theoretically simulate and model the behavior of these systems and in this way, help in the design of further experiments.