Toward the design of a motion-free tunable coupling module for varying spatial beam profiles: foundations of optimal coupling of a Gaussian mode into a fiber collimator with a dynamic two-lens system.

Abstract

In this paper, we present analytical expressions for the coupling of the fundamental Gaussian mode into a fiber collimator (FC) using a two-lens system. For this two-lens system, we also derive the limiting condition imposed on the focal lengths of the two individual lenses and their mutual separation for near-to-perfect mode coupling into the FC. Variations in the spatial mode profile of a Gaussian beam may occur due to various reasons. These include controlled changes in the beam profile inside mode-division multiplexed systems, and undesired spatial profile variations in beams that pass through turbulent media. The necessity of a dynamic mode-coupling module is dictated by the need to optimally couple Gaussian beams with dynamically changing spatial profiles. Using the analytical expressions derived for mode-coupling efficiency and the resulting lens separation condition that is imposed on a two-lens coupling system, we propose the design of a dynamic two-lens mode-coupling system with a pair of electronically controlled tunable lenses. The proposed dynamic coupling module is motion free and involves the movement of bulk components in order to achieve optimal coupling. The experimental results are also presented to verify the theoretical claims and the working principle of a two-lens mode-coupling system. The results of the experiments are discussed in detail and an excellent agreement is demonstrated between the proposed theoretical framework and the experimental results.