1. Date of download: 7/8/2016 Copyright © 2016 SPIE. All rights reserved. Simulation results using the hill-climbing algorithm for comparison with Fig. 3. Figure Legend: From: Novel fiber optic alignment strategy using Hamiltonian algorithm and Matlab/Simulink Opt. Eng. 2003;42(8):2240-2245. doi:10.1117/1.1586706

2. Date of download: 7/8/2016 Copyright © 2016 SPIE. All rights reserved. The coupling between eight-channel arrayed fiber optic devices. (a) Schematic of arbitrarily decentralized channels of the fiber array, while the light source channels were assumed to have perfect pitches. (b) Simulation result of alignment trajectory: the eight- channeled device move from an initially unaligned position to an optimal coupling position. Figure Legend: From: Novel fiber optic alignment strategy using Hamiltonian algorithm and Matlab/Simulink Opt. Eng. 2003;42(8):2240-2245. doi:10.1117/1.1586706

3. Date of download: 7/8/2016 Copyright © 2016 SPIE. All rights reserved. Simulation results using the Hamiltonian algorithm for a laser diode (LD)-fiber butt coupling with multiDOF alignment. The convergence trajectory of the fiber tip on (a) x DOF, (b) y DOF, (c) angular (pitch or yaw) DOF, and (d) the coupling efficiency versus alignment steps. Figure Legend: From: Novel fiber optic alignment strategy using Hamiltonian algorithm and Matlab/Simulink Opt. Eng. 2003;42(8):2240-2245. doi:10.1117/1.1586706

4. Date of download: 7/8/2016 Copyright © 2016 SPIE. All rights reserved. Simulation block diagram of a Hamiltonian algorithm: (a) basic blocks of the closed loop system, and (b) a Matlab/Simulink diagram for simulating the application of a Hamiltonian algorithm on the fiber optical alignment. Figure Legend: From: Novel fiber optic alignment strategy using Hamiltonian algorithm and Matlab/Simulink Opt. Eng. 2003;42(8):2240-2245. doi:10.1117/1.1586706

5. Date of download: 7/8/2016 Copyright © 2016 SPIE. All rights reserved. Schematic of a laser diode to a fiber coupling with 6 DOF. Figure Legend: From: Novel fiber optic alignment strategy using Hamiltonian algorithm and Matlab/Simulink Opt. Eng. 2003;42(8):2240-2245. doi:10.1117/1.1586706

6. Date of download: 7/8/2016 Copyright © 2016 SPIE. All rights reserved. Simulation results of the Hamiltonian algorithm for eight-channel arrayed fiber optic device alignment. The convergence trajectory of the center of channel 1 on (a) x DOF and (b) y DOF, (c) the convergence trajectory on roll angular DOF, and (d) the coupling loss of each channel after alignment. Figure Legend: From: Novel fiber optic alignment strategy using Hamiltonian algorithm and Matlab/Simulink Opt. Eng. 2003;42(8):2240-2245. doi:10.1117/1.1586706