Fig. 8: Acceptance angle as a function of the half-apex angles θ of the conical microlens.
The theoretical analysis is presented using three distinct colour lines to illustrate different scenarios. (1) When θ ≥ 43o, the green line represents the case in which light is directly emitted from the conical surface of the microlens without any reflection, and there is no hollow region within the emission pattern. However, the acceptance angle is too large ( > 60o). (2) When 31o ≤ θ < 43o, the cyan line represents the case in which light is directly emitted from the conical surface of the microlens without reflection. The acceptance angle is narrowed when θ goes smaller, but a hollow central region appears in the emission pattern. Equivalently, if the fibre collects light, the information in the central hollow region cannot be detected, which is unfavourable. The star highlights the working conditions used in our experiments, i.e., θ = 35o and an acceptance angle of 45o. By rounding the sharp tip of the cone, the hollow central region can be eliminated from the emission pattern (the inset in the lower right part). (3) When θ < 31o, the red line represents the case in which the light undergoes a single reflection (or hop) in the conical microlens. The hollow central region reappears and the transmitted light intensity is very low. Therefore, this case is not suitable for collecting the light
