Fiber Coupled Diode Laser Beam Parameter Product Calculation and Rule for Optimized Design

It is desirable to calculate the 'diagonal' (fiber) BPP, using the BPPs of the fast and slow axes before detailed design and simulation processes. A commonly used expression derived in an earlier work 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 component of the fiber BPP using BPPs of the fast and slow axes as input. Using the same simplified model we offer proof that the fiber BPP can be shown to have a minimum (optimal) value if certain rule between the conjugate variables of beam sizes and the numerical apertures along the two axes is obeyed. This optimization is easily calculated before detailed design and it offers valuable insights for the detailed design.