A production engineer (BS degree) and a technician (no degree) developed a practical method for measuring the pointing angle of laser diode before the laser diode is coupled with a single mode fiber. First, the total power of the laser diode (assuming A mW) is measured before the laser diode is fixed in the fixture. After the laser diode is fixed in the fixture, a small circular aperture (smaller than the beam waist) is centered at the mechanical axis of the fixture. The power of light passing through the aperture (assuming B mW) is measured as shown in Fig. 1. The pointing angle can be represented by the value of B/A. The larger is the pointing angle, the smaller is B/A. After the aperture is removed, the light is focused into a single mode fiber at the mechanical axis using proper optics. The coupling efficiency is defined as C/A, where C is the measured output power (in mW) from the single mode fiber. The effect of the pointing angle of laser diode on the coupling efficiency is shown in the table of C/A versus B/A.

Fig. 1.

Measurement setup, θ: pointing angle.

The power of light after passing through the aperture as a function of d (see Figs. 1 and 2) can be calculated, provided that the laser diode beam has been corrected to a circular Gaussian beam [1]. The Gaussian intensity is I(x,y) = I₀ exp{-[2(x+d)²+2y²]/α²}, where α is the beam waist, and I₀ = 2A/παa² (remember A is the total power). The power , where a is the aperture radius, and . Although B or P(d) cannot be derived analytically, it can be calculated and plotted using a mathematical software such as Mathcad. Therefore, we can calculate the pointing angle θ from the value B/A.

Fig. 2.

Positions of laser beam and aperture on aperture plane.

In conclusion, we have shown how to improve a practical qualitative method developed by an engineer and a technician in a real production facility to an academic quantitative method using a theoretical analysis and a mathematical software such as Mathcad. This will be a good teaching material in the class.