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A new type of fiber for distributed filtering is proposed, designed to have resonant coupling between core and cladding at desired wavelengths. Design principles are illustrated with simulations of several fibers. A filter fiber was fabricated following this design strategy. Measured transmission spectra and imaging of mode output confirm the expected resonant coupling between core and cladding near 1100nm.
©2005 Optical Society of America
1. Introduction
Distributed filtering is important in many fiber optical systems, and is particularly key for amplifiers, where undesirable noise components are amplified along the length of the gain fiber. In an amplifier or laser system, amplified noise wastes pump power and can potentially overwhelm the desired signal, even if noise wavelengths are subsequently removed. For this reason, use of distributed filtering along the gain medium has been studied, for example, in L-band amplifiers [1, 2, 3].
Filtering has been demonstrated in bandgap fibers with two-dimensional (2D) lattice [4, 5, 6] or one dimensional concentric ring geometries [7, 8]. In these fibers, the basic confinement mechanism is a very wavelength-dependent bandgap effect, and so filtering of transmitted light is a natural outcome. In order for the bandgap guidance mechanism to dominate, one must avoid significant index guidance, and so eliminate any raised-index features in the core region. At the same time, for gain applications, the core would need to be doped with a gain material, such as erbium or ytterbium. In priciple, one could achieve a zero-index-contrast amplifying core by balancing the concentration of co-dopants.
Here, we present an alternative type of filter fiber, where guidance is provided by a standard core, and filtering is provided by resonant coupling to leaky cladding modes [9]. The physical structure and filtering action have similarities to the concentric-ring bandgap type filter fibers [7], but the intentionally up-doped core leads to important differences. This extention to designs with nonzero index contrast at the core is important because they provide additional design control, and also because a perfectly uniform index may be difficult to achieve in practice.
In this paper, we explore the basic guidance properties and some design tradeoffs with numerical simulations. We then present measurements of a filter fiber fabricated according to this strategy. This fiber has a low-contrast core surrounded by two high-index rings, and demonstrates filtering by wavelength selective coupling to the cladding.
2. Filter fiber design principles
The filter concept [9] is illustrated in Fig. 1, where we see raised-index guiding features in both the core and cladding regions. The coupling behavior is conceptually no different from a simple asymmetric dual-core fiber [10, Chap. 13.9]: at most wavelengths light propagates in weakly perturbed modes of the individual waveguiding features. At the particular “resonant” wavelengths, where index-matching of modes occurs, however, light propagates in mixed modes, and energy can freely flow between the features. Light in the core then sees coupling to the cladding that can be strongly wavelength dependent.
This concept can be implemented using a number of fiber geometries. For example, Fig. 2 shows a raised index core surrounded by different claddings. In each case, the individual cladding features can be “tuned” to provide filtering at a desired wavelength by providing nearly index-matched coupling between core and cladding at that wavelength.
Figure 3 illustrates mixing of core and cladding modes at an index-matching wavelength. It schematically shows the effective index versus wavlength curves for a core and cladding mode. At wavelengths where these effective index values are nearly equal, power mixes between the core and cladding waveguides. By itself, this coupling between core and cladding does not imply any loss (and then, no filtering). However, if the cladding modes are leaky, wavelengths coupled from core to cladding can be effectively filtered out. A similar mechanism was discussed in [11], but there, light was filtered according to transverse mode, not wavelength.
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.
3. Numerical design: core-ring fiber
We now illustrate this filter concept using simulations of a simple design family, with a concentric raised-index core and a single raised-index cladding ring. The core-ring family is easily produced by standard MCVD fabrication, and provides suitable flexibility for designing a filter fiber. In particular, it demonstrates how filter properties can be controled by cladding features, allowing substantially independent control of signal-wavelength properties by core design. Aside from the outer cladding index n clad, the design has 5 paramters: the core radius R core and contrast Δcore largely determine relevant properties in the pass-band (such as effective area and effective index of the fundamental core mode), while the ring thickness t ring, and contrast Δring largely determine the filter wavelength. The final parameter, ring radius R ring, can be used to tune the bandwidth of the filter (related to the strength of coupling between core and ring, as discussed below). Below, we use standard definitions Δn = n - n clad and Δ = (n 2 - )/(2n 2) ≈ n cladΔn. The simulations of this section were done using the transfer matrix approach [12].
3.1. Index-matched coupling for a core-ring fiber
We have performed many simulations which support the basic idealization of weakly-coupled core and ring modes, with mixed modes appearing at index-matching regions only. This is indicated by the effective index, loss, and mode intensity profiles of the simulated modes.
For example, Fig. 4 shows three effective index vs. wavelength plots that illustrate the mode-coupling concept: on the left, we see modes of a step-index core only (no ring) with R core = 15μm, Δn core = .0015. These values are in the range of few-moded, large-core fibers of interest in amplification. In the middle plot, we see some modes of a fiber with high-index ring only (no core), with t ring = 2.6μm, Δn ring = .02, and R ring = 19μm. Only modes of rotation number 1 (the fundamental-like symmetry class) have been included here. We can see that, in the neighborhood of 1100nm wavelength, a ring mode falls to low index and is cutoff. Note that the vertical scale is very different from the core-only modes, so any crossing of mode lines will occur near the bottom of the center plot. In the right plot, we see modes of a fiber with both core and ring (blue for rotation number 1, red for rotation numbers 0 and 2) along with guidelines repeating the core-only (black dashed) and ring-only (green) modes for comparison. In the vicinity of the ring-mode cutoff, there is an index-matching point where the ring mode crosses each core mode. For the most part, modes of the core-ring structure follow either the core-mode or ring-mode guidelines. However, modes near the index-matched intersection points deviate from these guidelines, as they make continuous transitions between the two. This is indicative of coupling between two waveguides; the core-like mode continuously changes into a ring-like mode as wavelength varies, with mixed modes appearing in the transition range of wavelengths. This type of dynamics has been discussed recently for different types of fiber [13, 14, 11].
Figure 5 further shows that modes near the index matching point are indeed a mixture of pure core and cladding modes. A close-up of the effective index plot is shown along with intensity plots for four selected modes of the core ring structure. Away from the index-matching point, we see that light is well confined to the core, while at the index-matching wavelength, light is distributed across both core and cladding.
3.2. Adjusting the spectrum of mixed modes
The filtering spectrum can be easily adjusted through proper choice of cladding geometry. The most straightforward adjustment is the index-matching wavelength that determines where spectral features occur. In Fig. 6, we see the index-matching wavelength plotted as a function of ring thickness,with all other parmeters following the example of Fig. 4. As expected, changes in ring thickness shift the ring-mode cutoff (with cutoff wavelength roughly proportional to ring thickness), and the index-matching point along with it.
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.
Bandwidth is another important filter parameter, and is determined by the strength of coupling between core and cladding modes: if the coupling is weak, even a very small index mismatch can disrupt the transfer of power between the waveguiding regions. Figure 7 illustrates this with index-matching plots for two fibers similar to our first example. Again R Core = 15μm, Δn core = .0015, t ring = 2.6μm, and Δn ring = .02, but but the ring separation is varied: R ring = 18μm (left) and R ring = 22.0μm (right). The plots show that as separation is increased (and coupling between core and cladding becomes weaker) the wavelength range becomes narrower where modes deviate from “pure” core and cladding curves. Bandwidth can therefore be designed by adjusting separation, for example, although it is effected by other fiber parameters. More complicated spectra could be engineered, for example, by arranging multiple index-matching points between the core and cladding features with differing geometries (as in Fig. 2(c)).
3.3. Filter fiber transmission, gain, and loss
In general, even if light couples from the core to the cladding, it can return back to the core instead of being filtered out. However, a fiber can be designed so that this light is “lost,” or sees reduced gain, once in the cladding. This differential transmission can be arranged using several mechanisms: Typically light in the cladding will automatically see reduced gain overlap (since gain dopants are in the core), but this light can also be subject to increased absorption, scattering, leakage, or bending losses. In addition, input and output coupling to the fiber may provide an additional bulk loss due to mode overlap.
Figures 8–9 presents simulations for a simple example where losses result from absorption in the cladding ring. This one-ring design has R core =5.8μm, Δn core =.002t ring =4.4μm, Δn ring = .01, and R ring = 15μm, and highlights the relationship between absorption losses and core-ring coupling. Figure 8 shows the the index profile and effective index vs. wavelength, showing similar mode transitions to the previous larger-core example. The absorption loss estimates of Fig. 9 includes four field profiles at selected wavelengths (indicated by red dots). These show that high-loss regions do indeed correspond to mixed modes (with significant power in the cladding ring) in the index-matched region, while low-loss modes resemble an ordinary fundamental-like core mode away from index-matching. In fact, for reasonably low losses, absorption will simply be a perturbation nearly proportional to the fraction of light propagating in the ring [15], so the correspondence of Fig. 9 between power fraction in the ring and modal loss is not surprising. A similar correspondence would be expected for localized scattering introduced at the ring.
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.
Bend-induced losses are more complicated: In principle, bend losses are straightforward to calculate numerically. For example, the finite difference method, can be used, along with an equivalent index profile [16] of the fiber with bend radius R bend:
However, bending causes a number of changes that make the loss spectrum more complicated than for absorption-based filtering: The ring modes themselves are substantially changed, and the symmetry is modified, breaking degeneracies and allowing many more distinct ring modes to couple to the core. Resonant loss peaks will be superimposed on the well-known fundamental cutoff induced by the bend [17]. Many numerical methods (including the 1D trnasfer-matrix method, the multipole method, and the periodic plane-wave expansion method) clearly cannot handle bends without significant modification or additional approximations. Finally, to compare with measured transmission spectra, one needs to extract a single loss value from the many calculated modes. By the very nature of the cladding-coupling strategy, mixed modes play an important role in the losses, so the most important wavelengths have more than one mode overlapping with the fundamental, often with very different modal loss values. To extract a single composite bend loss from the multiple bend losses αj of the filter fiber modes, we can write some general expressions,
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.
But these expressions require mode-coupling overlap parameters at the input I input,j and output I j,output. These are generally not known, but qualitative estimates can be obtained in order to compare to measurements.
4. Fabricated filter fiber
A filter fiber based on this principle was designed and fabricated with the measured index profile shown in Fig. 10. This fiber was designed to have an index-matching point (and thus a loss peak) at a wavelength around 1100nm. Fiber index profiles were measured at 546 nm using the Transverse Interferometric Method (TIM) as described by Marcuse [18, Chapter 4]. The fiber was drawn to two sizes, with 80 micron and 100 micron outer diameters, with nearly identical index profiles as a function of the normalized radius (radius over the outer diameter).
Fig. 10. A fiber was fabricated with raised-index core and two cladding rings. Measured index profile is shown vs. radius.
The spectral attenuation and bend loss of the distributed fiber filter were measured for both 80 μm and 100 μm fiber, and showed the expected shifts in spectral features according to scaling. All optical measurements were performed using illumination from a white light source and detected with an ANDO AQ-6315A optical spectrum analyzer. For both transmission and bend loss measurements, both the input and output ends of the filter fiber were spliced to SMF-28 with an 8μm core with core alignment. For the bend loss measurements, the total fiber length was 1.2 meters and bend diameter was 8.5 cm.
The transmission spectrum of an unbent section of filter fiber, is shown in Fig. 11, displaying a sharp drop in intensity near 1100 nm. As mentioned above, white light is coupled into the core of the filter fiber and collected through spliced connections to SFM-28, so the observed transmission only accounts for light propagating in the core of the filter fiber. To determine the effectiveness of the Ge-ring regions in coupling light out of the core, we performed mode field imaging studies of the output of the filter fiber. In this experiment, white light was coupled into SMF-28 which was spliced to the filter fiber with the cores aligned. Using an Ericson 905 splice for alignment, an SMF-28 fiber was butt coupled to the filter fiber output and spectral intensity was recorded using and OSA. The OSA was set a fixed wavelength while the SMF-28 fiber was scanned across the endface of the filter fiber by stepping the splicer motor manually. The change in intensity in the spectral output corresponds to the light intensity as a function of fiber radius, providing a 1-dimensional image of the mode field intensity. Figure 12 shows the resulting mode imaging for both 1100 nm and 1500 nm. At 1500 nm, only one gaussian shaped peak is observed, demonstrating that the guided light within the filter fiber is confined to the core. At 1100 nm, 5 peaks are observed with one larger central peak surrounded on each side by two less intense, narrower peaks, consistent with light being guided in both the central core and the two outer Ge ring regions. The maximum intensity of the central feature is 14 dB less than for the peak at 1500 nm, which agrees with the tranmssion spectrum in Fig. 12. The transmission and mode imaging measurements provide a clear picture of the coupling mechanism of the filter fiber. At 1500 nm, the core and Ge-ring regions are not coupled and the light guides in the core unperturbed. At the resonant wavelength, near 1100 nm, the light couples out of the core region into the Ge-rings.
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.
Bend loss measurements in Fig. 13 reveal a more complicated spectrum with several sharp loss peaks. The features at 583 and 1070 nm do not increase linearly with number of bends. A general onset of sharp bend loss features above around 1100nm wavelength is also seen in finite difference simulations, although detailed agreement was not obtained for this structure. In Fig. 14, the simulated straight-fiber effective index and bent-fiber loss spectra are shown for bend radii 4.25cm and 5.5cm, using the measured index profile of Fig. 10. The two-ring structure has two index-matching points in the 1000-1200nm region. Tighter bending not only increases overall losses, but causes broading and splitting of spectral features. Because the fiber is very sensitive to macrobends, to small changes in index profile, and to mode coupling between its many guided modes, it is not surprising that quantitative modeling is difficult. Accurate microbending models are generally empirical even for much simpler single-mode fibers. While current models provide useful, rough guidelines for design, ongoing work will aim to improve modeling accuracy.
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).
5. Conclusions
We have designed, fabricated, and measured a novel type of distributed filter fiber based on the principle of resonant coupling between core and cladding. Transmission and bend-loss measurements confirm that basic filtering function can be incorporated into a fiber with standard fabrication technology. Simulations show that this general class of designs can provide distributed filtering in a design space relevant to high-power optical amplifiers.
Acknowledgments
We thank David DiGiovanni, Marc Mermelstein, Cliff Headley, and Matt Andrejco for useful conversations. This work was supported in part by the NIST ATP program under award number 70NANB4H3035.
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