2. Optical design and relevant ray paths of the fiber combiner
A schematic side view of the side-pump combiner consisting of a pump feeding fiber (PFF), a coreless intermediate fiber (IF) and a target fiber (TF) is shown in Fig. 1
Fig. 1 Schematic side view of a side-pumped double-clad fiber including important ray paths.
. The diameter of the PFF core and the cladding was 105 and 125 µm, respectively. The NA of the pure silica PFF core used in the simulations was 0.15, 0.22 or 0.3 and, therefore, the refractive index of the PFF cladding was depressed in comparison to the refractive index of the PFF core. The cladding of the PFF was surrounded by a polymer coating only for mechanical protection of the fiber. Therefore, the PFF preserved the same waveguide properties after removal of the polymer coating. In the case of side-pumping without an IF, the higher refractive index of the core of the PFF would suppress the pump power transfer into the TF as long as the PFF is untapered. An increase of the NA of the pump light due to tapering of the PFF would result in an increase of the pump power transfer, though only for rays that exceed the NA of the PFF core. Thus, it is especially difficult to couple pump light rays with a low NA into the TF. Unfortunately, this type of PFF is typically used as high power delivery fiber of pump diodes. To overcome this problem, without removing the glass cladding of the PFF, a coreless IF was inserted in the fiber combiner setup. At first the ~30 cm long IF with a cladding diameter of 125 µm was fusion spliced to the PFF. The IF had a NA of 0.46 due to the refractive index difference (Δn) between fused coupler silica and the outermost polymer coating. After removing the polymer coating (e.g. with acetone) along a certain section of the IF (~15 mm), the IF was individually tapered, and afterwards the converging taper portion was laterally fused with the TF. The fusion level (FL) is defined as FL=(2z)/(dIF+dTF), where dIF and dTF are the cladding diameters of the IF and the TF at a certain taper position, respectively, and z represents the distance of the fused IF and TF, as depicted in Fig. 1. The FL was experimentally determined by measuring dIF, dTF and z at different positions along the converging taper portion with an optical microscope. With this measurement an averaged very low FL of 1.99 was determined, which was also used for the simulations. The overlap area between the TF and the IF is defined as the fusion zone. In contrast to the converging taper portion, the diverging taper portion of the IF was not fused to the TF, but placed under a small angle to the fiber axis of the TF, resulting in a small air gap between the IF and the TF. The employed TF was a DC fiber with a core diameter of 25 µm (NA 0.06) and a cladding diameter of 250 µm (NA 0.46). The cladding of the TF was also surrounded by a polymer coating, except along the coupling region of the combiner. The low index coating had to match the mechanical and additionally the optical properties of the DC fiber. An anchoring bond was used to fix the fiber bundle on each side on a copper substrate. Figure 1 shows the anchoring bond only on the right-hand side without the copper substrate. Additionally, the anchoring bond served as a pump light stripper for rays which do not satisfy the NA criterion of the TF.
Before proceeding with a more detailed investigation with the aid of simulations in the next section, we will qualitatively discuss some important ray paths of the fiber combiner. Pump light rays guided into the PFF and entering the tapered portion of the IF increase in NA as long as the rays propagate along the converging taper. As a rule of thumb, the pump light input NA increases by a factor of the taper ratio (TR), which is defined as the ratio of the original fiber diameter to the diameter of the taper waist. Pump light coupling into the TF occurs as soon the rays enter the fusion zone. The converging taper portion increases the probability for pump light transfer into the TF, since the number of ray-bounces along the lateral surface of the IF increases. Particularly, pump light rays with a low input NA couple more efficiently due to the converging taper.
Pump light rays remaining in the IF, and consequently not coupling into the TF, can occur as transmitted power (TP: transmittedpower, Fig. 1) or power leakage into the ambient air (PAA: power leakage into the ambient air, Fig. 1). As long as the condition for internal total reflection is satisfied, the pump light rays are detected as TP, otherwise the rays escape into the ambient air as PAA. The angle of total internal reflection for the uncoated IF is 43.6°, since Δn between fused silica and air is 0.45 at a wavelength of 976nm pump laser protector, which means the IF can guide light up to a theoretical NA of 1.05. Of course, the NA cannot exceed 1.0. Therefore, pump light rays with a theoretical NA in the range of more than 1.0 up to 1.05 would experience total reflection in the case of an existing fiber endface. Pump light rays which exceed the theoretical NA of 1.05 occur as PAA.
For almost loss-free pump light coupling into the TF it is necessary that the rays enter the TF before they exceed the cladding NA of the TF of 0.46. This desired coupling behavior can usually be achieved by adapting the taper parameters. However, pump light coupling for rays with an NA far above 0.46 cannot be completely suppressed. Unfortunately, this pump power leakage couple into the coating of the TF (PCT: power leakage into the coating of the target fiber) and can damage it.
In summary, the input pump combiner will be divided into the coupled pump power and the losses including PAA, PCT and TP (Fig. 1).
