Alignment of Optical Axes Positioned with Multiple Degrees of Freedom by Hamiltonian Algorithm

Abstract

In optical fiber telecommunications, optical axes of optical devices that transmit light must be accurately positioned so that when many devices are connected, the transmitted light intensity can be maximized. In coupling of optical fiber arrays and planar waveguides, many optical axes must be positioned with multiple degrees of freedom. This is a large-scale, and complicated problems; (1) searching optimal positions for systems with multiple degrees of freedom, (2) trapping at local minima for optical beam profiles with satellite peaks, and (3) ensuring robustness against disturbance from mechanical equipment, (4) constrained optimization required in aligning array devices. We examine the use of the Hamiltonian algorithm to quickly align optical axes that must be precisely positioned with multiple degrees of freedom. The Hamiltonian algorithm utilizes the mixing properties of a dynamical system and efficiently searches for the global minimum of the objective function in optimization problems. We discuss the effects of mixing properties and degrees of freedom, when searching for the global minimum. We also show that our technique can avoid trapping at local minima, and that it is robust against disturbance. Moreover, we examine whether our method can be used to couple optical array devices such as fiber arrays, and show that we can quickly find the optimal points, at which the maximum optical intensities are obtained.