Fig. 1. These schematic waveguide plots illustrate the concept of filtering due to resonant coupling between core and cladding modes. High-index waveguiding features in the core and cladding regions are associated with local modes (red and green lines). In the left plot, the effective index values (dashed lines) for core and cladding modes are different, and coupling is frustrated. For the same waveguide, there is a resonant wavelength (right plot) such that the the effective index of core and cladding modes are matched. Light in the core can then efficiently couple to index-matched (and possibly leaky) cladding modes.

Fig. 2. The filter fiber concept proposed in this paper can have a wide variety implementations. Perhaps the simplest implementations use a few identical high-index inclusions (a) or rings concentric with the core (b) to guide cladding modes. Naturally, more complicated cross sections, for example (c) can be designed using similar principles.

Fig. 3. In this schemeatic effective index plot, curves for “pure” core modes and cladding modes cross. Exact modes of the waveguide will resemble core or cladding modes away from this index-matching point, but mixed modes will result for wavelengths close to index-matching.

Fig. 4. Effective index plots for three structures illustrate the coupling of core and ring modes. Modes are calculated for the core only (left), for the ring only (center) and for the core-ring fiber (right, blue and red; green and black guidelines indicate core-only and ring-only plots for comparison). Modes of the core-ring structure make a transition from being core-mode-like to ring-mode-like as wavelength varies across the index-matching point.

Fig. 5. A closeup of the effective index plot is shown along with intensity plots for selected modes (black stars). The intensity plots resemble simple fundamental core modes away from the index-matching point, but extend through the core and cladding ring near the index-matching wavelength.

Fig. 6. The index-matching wavelength (solid line) can be tuned by adjusting the ring thickness t _ring of the fiber in the preceeding example. Since the ring has index contrast much larger than the core, the index matching curve essentially follows the cutoff wavelength of the ring mode (dashed), roughly proportional to thickness.

Fig. 7. The wavelength and bandwidth of the mixed-modes can be adjusted by modifying the fiber design. Effective index vs. wavelength for fibers similar to the above example show bandwidth narrowing as ring radius R _ring is increased, and filter wavelength changing in proportion to ring thickness t _ring.

Fig. 8. Simulated modes shown in the effective index plot (left) result form the fiber index profile (right). The dark blue lines belong to the symmetry class with rotation number 1, and show anti-crossing at the index-matching point.

Fig. 9. Narrowband loss accompanies coupling between core and cladding if absorption (or scattering) is incorporated into the ring material. A sharp loss peak corresponds to the index-matching wavelength. Mode-mixing at the loss peak is evident in the inset intensity plots.

Fig. 10. A fiber was fabricated with raised-index core and two cladding rings. Measured index profile is shown vs. radius.

Fig. 11. Transmission spectrum of dual ring 80 micron fiber with both input and output spliced to SMF fiber.

Fig. 12. One-dimensional imaging of 80 micron fiber output by scanning an 8 micron core SMF fiber across the output endface at 1100 nm (blue) and 1500 nm (dashed). At 1100 nm the light is clearly coupling out of the core and into the Ge-doped ring regions, while at 1500 nm, the light remains in the core.

Fig. 13. Total measured bend loss is shown for a filter fiber with core and two cladding rings, bent to 8.5 cm diameter. Several high-loss resonant features are observed above 1100nm wavelength.

Fig. 14. The index-matching plot (left) shows the ideal core mode (dashed) intersecting with distinct inner-ring and outer-ring modes. The total simulated bend loss through three loops wound onto a radius of 4.25 cm and 5.5 cm is shown (right).