Expanded Jones complex space model to describe arbitrary higher-order spatial states in fiber

Abstract

As a new multiplexing dimension, spatial modes are catching increasing attentions nowadays. It is a fundamental task to establish an appropriate theoretical model to describe these spatial modes, especially higher-order spatial modes. However, existing theoretical models are only able to explain some special higher-order spatial states in fiber. The basic problem in these models is that their discussed dimensions are not enough. Indeed, to describe a higher-order spatial state, at least four dimensions are needed. In this paper, we present an expanded Jones complex space model, which is four-dimensional when a single higher-order state is discussed. The expanded Jones model is based on the discussion of an arbitrary combination of four degenerated higher-order modes. As a result, arbitrary spatial states are described. Because the number of used dimensions matches that of the problem, the descriptions of higher-order modes are more complete than other models. Also, we have verified the reliability of the expanded Jones model in our experiment. This model has the potential to simplify many analyses related to spatial modes in fiber.