Thermal aberrations and structured light I: analytical model for structured pumps and probes

Structured light, where optical beams are tailored in amplitude, phase and polarisation to some desired profile, has become topical of late, fuelled by the ease at which such fields can be created internal and external to the source. In this treatise, part I of a two part series, we consider the thermal effects (stress, lensing and phase aberrations) associated with high-power structured light, where the structure may be the pump, optically inducing the thermal effects in the medium, or the probe, experiencing thermally induced optical aberrations. We outline a general theory for arbitrary structured light pumps and probes, reducing to the prior studies of Gaussian and flat-top beams as special cases. We illustrate the power of the model using the structure of light as a new degree of freedom with which to mitigate thermally induced optical aberrations. Finally, in part II of this composite work (Scholes and Forbes, Appl Phys B, 2021. https://doi.org/10.1007/s00340-021-07656-z ), we experimentally demonstrate the phase aberration predictions using a digital micro-mirror device for real-time simulation of such high-power thermal effects in a cheap, fast and versatile manner, without the need for elaborate high-power experiments. Our work brings together the disparate fields of thermal modelling and structured light, providing a framework for future work in the creation and delivery of high-power structured light fields.