Non-Uniqueness of Non-Linear Optical Response

In recent years, non-linear optical phenomena have attracted much attention, with a particular focus on the engineering and exploitation of non-linear responses. Comparatively little study has however been devoted to the driving fields that generate these responses. In this work, we demonstrate that the relationship between a driving field and the optical response it induces is non-unique. Using a generic model for a strongly interacting system, we show that multiple candidate driving field exists, which will all generate the same response. Consequently, it is possible show that the optical response is not sufficient to determine the internal dynamics of the system, and that different solutions for the driving field will do different amounts of work on a system. This non-uniqueness phenomenon may in future be utilised to engineer internal system states without modifying its optical response.