- High-NA Fibers Enable High-Power Lasers
A research group at the University of Bath in the UK has analyzed and demonstrated techniques to fabricate photonic crystal fibers (PCFs) with a numerical aperture as high as 0.9. The techniques may dramatically affect the efficiency and power of fiber lasers and may be useful in collecting radiation in fluorescence-monitoring applications.
A simple optical fiber consists of a high-index core surrounded by a lower-index cladding. If the core is doped with a lasing ion, pump light coupled into the core can create a population inversion in the ions, and if reflectors are placed on both ends of the fiber, it can lase. A limitation of this scheme is that it is difficult to couple light from highly divergent diode lasers into the tiny core, which typically is 10 or 20 µm in diameter.
To overcome this limitation, developers of early versions of fiber lasers fabricated double-clad fiber, which consists of the core, and an inner and an outer cladding. Pump light was coupled not into the tiny core, but into the larger inner cladding, where it overlapped the core to create a population inversion.
A more recent development is the photonic crystal fiber, or "holey fiber." In a PCF, the core and the cladding are made of the same material, but a regular system of longitudinal airholes reduces the average refractive index of the cladding. Thus, with the index of the core greater than that of the cladding, light still is guided in the core of the fiber by total internal reflection.
One of the unique properties of PCFs is that the single-mode core can be significantly larger than that of a conventional fiber. In a high-power fiber laser, a larger mode-area core means that the same power density in the core can be scaled to a higher laser output without optical damage or deleterious nonlinear effects.
Researchers also have developed double-clad PCFs for use in lasers. These consist of a solid core, an inner cladding with an array of relatively small airholes, and an outer cladding with an array of larger airholes. Although the average index of the outer cladding -- calculated from the geometric air-to-glass ratio -- is much smaller than the index of the inner cladding, the numerical aperture of the inner cladding is not correspondingly large.
Figure 1. The solid curve is the numerical aperture predicted by a simple slab model. The circles, squares and triangles are the results predicted by full eigenmode calculations of the fibers in Figures 2a, 2b and 2c, respectively. The filled triangles are experimental results with a PCF fiber, and the crosses are experimental results with two different solid-cladding fibers. ©2004 IEEE.
Now the Bath researchers have applied a more sophisticated mathematical model of double-clad PCFs and have shown that it is the structure of the outer cladding, not its simple average index, that determines the numerical aperture of the inner cladding. They modeled the outer cladding as a system of uncoupled slab waveguides and calculated the effective refractive index for that system. They calculated the inner cladding's numerical aperture from the standard formula NA = (ni2 – no2)1/2, where ni and no are the indices of the inner and outer claddings, respectively.
The results are shown by the solid curve in Figure 1. The horizontal axis of this figure is the width of the individual glass waveguides in the outer cladding (normalized to the wavelength of the light in the fiber). Obviously, the width of these structures is crucial. The double-clad PCFs in earlier experiments had glass thickness in the outer cladding on the order of, or larger than, the wavelength of the light in the fiber -- approximately 1 µm. Despite the low average index of the outer cladding, the numerical aperture of the inner cladding was disappointingly low.
Figure 2. A detail of the four types of PCF analyzed shows the jacket, outer cladding and inner cladding. Only the type of fiber shown in the d frame can support both a large-mode-area core and a large-numerical-aperture inner cladding. ©2004 IEEE.
But a complication arises when designing double-clad fibers whose outer claddings have glass structures narrower than 1 µm. In any PCF whose outer cladding is penetrated by a system of airholes, the physical criteria that the fiber must meet to have a large-mode-area core are incompatible with the thin-wall requirements for a high-numerical-aperture inner cladding. That is, fibers structured like those in Figures 2a- 2c cannot simultaneously have a large-numerical-aperture inner cladding and a large-mode-area core. However, because the outer cladding of the fiber in Figure 2d is not a simple stacked structure but instead is stretched, its walls can become arbitrarily thin by stretching them as much as needed. This fiber simultaneously can realize a large-mode-area core and a large-numerical-aperture inner cladding.
Figure 3. The micrographs display a conventional solid-cladding fiber suspended in a web of thin silica bridges. The individual bridges are approximately 220 nm thick. ©2004 IEEE.
To corroborate their assumption of a simple slab model, the researchers performed full eigenmode calculations to obtain the numerical aperture of the fibers in Figure 2. The results are shown in Figure 1 as the circles (for the fiber in Figure 2a), hexagons (Figure 2b) and triangles (Figure 2c). The more complex calculations are in good agreement with the simple model for the fiber in Figure 2b. The other two fibers have significantly more glass in their structures than assumed in the simple slab model and, thus, agree less well with the model.
Figure 4. The micrographs display a PCF fiber suspended in a web of thin silica bridges. The individual bridges are approximately 230 nm thick. ©2004 IEEE.
To verify their predictions, the researchers measured the numerical aperture of a number of fibers with stretched outer-cladding structures like those in Figures 3 and 4. These results are shown in Figure 1 as crosses (for two solid-cladding fibers of the type shown in Figure 3) and as the filled triangles (for a PCF fiber as shown in Figure 4). The experimental data strongly support the theoretical predictions.
- The emission and/or propagation of energy through space or through a medium in the form of either waves or corpuscular emission.
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