Fiber coupled diode laser beam parameter product calculation and rules for optimized design

The Beam Parameter Product (BPP) of a passive, lossless system is a constant and cannot be improved upon but the beams may be reshaped for enhanced coupling performance. The function of the optical designer of fiber coupled diode lasers is to preserve the brightness of the diode sources while maximizing the coupling efficiency. In coupling diode laser power into fiber output, the symmetrical geometry of the fiber core makes it highly desirable to have symmetrical BPPs at the fiber input surface, but this is not always practical. It is therefore desirable to be able to know the 'diagonal' (fiber) BPP, using the BPPs of the fast and slow axes, before detailed design and simulation processes. A commonly used expression for this purpose, i.e. the square root of the sum of the squares of the BPPs in the fast and slow axes, has been found to consistently under-predict the fiber BPP (i.e. better beam quality is predicted than is actually achievable in practice). In this paper, using a simplified model, we provide the proof of the proper calculation of the diagonal (i.e. the fiber) BPP using BPPs of the fast and slow axes as input. Using the same simplified model, we also offer the proof that the fiber BPP can be shown to have a minimum (optimal) value for given diode BPPs and this optimized condition can be obtained before any detailed design and simulation are carried out. Measured and simulated data confirms satisfactory correlation between the BPPs of the diode and the predicted fiber BPP.