Photonic crystal fibers are highly attractive as nonlinear media as they combine a large nonlinear coefficient and a highly customizable zero dispersion wavelength - flexibility not found in any other medium. However, the high dispersion slope at the zero-dispersion wavelength demonstrated so far is very limiting to the useful bandwidth. We propose a new fiber design comprising a hybrid core-region with three-fold symmetry that enables unprecedented dispersion control while maintaining low loss and a high nonlinear coefficient. The lowest dispersion slope obtained is 1·10-3ps/(km·nm2) or one order of magnitude lower than for conventional slope reduced nonlinear fibers. The nonlinear coefficient is more than 11 (W·km)-1 and loss below 7.9 dB/km at 1.55 µm has been achieved.
©2003 Optical Society of America
Nonlinear photonic crystal fibers (PCFs) were among the first fiber types to demonstrate the advantages of the PCF technology  and they have since then proved their worth in numerous applications among which supercontinuum generation is the most studied. With the introduction of the nonlinear telecommunication PCF [2,3] the high index contrast and flexibility of the PCF technology was utilized to create a fiber with a very high nonlinear coefficient and zero dispersion at 1.55 µm. Although showing superior performance in applications like all-optical demultiplexing [4,5], the high dispersion slope of more than -2·10-1 ps/(km·nm2) limits the useful spectral bandwidth of the fiber. The demonstrated fiber featured an up-doped core for increased nonlinear coefficient. However, zero dispersion at 1.55 µm can also be achieved in pure silica fibers. In both cases, the dispersion slope is determined by the hole-size. The slope can be significantly reduced by lowering the ratio between hole-size, d, and pitch, Λ, but at the cost of a considerable increase in both effective area and confinement loss . Consequently, dispersion-flattened fibers with a d/Λ on the order of 0.25–0.3 will exhibit a nonlinear coefficient 5–10 times lower than a fiber with a slope of -2·10-1 ps/(km·nm2).
PCFs with very low and flat dispersion can also be realized by varying the hole-size radialy, going from small holes around the core to large holes in the last ring. However, this approach poses significant fabrication challenges and such designs have only been treated theoretically. 
The dispersion slope of standard nonlinear step-index fibers is on the order of 2·10-2 ps/(km·nm2). Reduction of the slope can be obtained by introducing a depressed cladding region around the core and fibers with a slope as low as 1.3·10-2 ps/(km·nm2) have been demonstrated . The limitation in this method of slope reduction is the index contrast between the core and the depressed cladding set by the obtainable doping levels.
In this paper we demonstrate a new type of nonlinear PCF that features full control of both dispersion level and dispersion slope while maintaining low loss, a high nonlinear coefficient and simple fabrication.
2. Fiber design and characterization
The fabricated fibers feature a three-fold symmetric hybrid core region comprising a germanium-doped center element (n=1.487) surrounded by three fluorine-doped regions (n=1.440) embedded in a standard triangular air/silica cladding structure (see Fig. 1). The diameter of the doped elements equals the pitch. Due to the shape of the core, the near field appears three fold symmetric (see Fig. 1 right), however, most of the power is carried in the central Gaussian-like part located in the up-doped center element resulting in a mode field diameter of approximately 3.5 µm. Consequently, coupling to standard step-index fibers is very efficient and the fiber can be spliced to step index fibers with a loss of 0.25 dB.
The hybrid core adds additional flexibility in the design of the dispersion compared to the well-known single core triangular cladding PCF. By varying the pitch and hole-size, it is possible to alter the balance between the negative waveguide dispersion contribution from the holes and the positive contribution from the down-doped regions, respectively. The sum of waveguide and material dispersion in the fiber can thereby be altered to obtain the desired dispersion profile (see insert in Fig. 2). The dispersion can be tuned to almost any combination of dispersion level and dispersion slope in the range 1400–1700nm, including zero dispersion and flat slope. The low slope can be maintained in a large wavelength range and it is possible to keep the dispersion variation within 1ps/(km·nm) over more than 200 nm. Nonlinear fibers with such a dispersion profile can pave the way for a range of new broadband tunable devices like tunable optical parametric amplifiers, wavelength converters, regenerators and all-optical demultiplexers - devices that, until now, have been limited to operation close to 1.55 µm.
The calculations shown in Fig. 2 illustrate how the dispersion can be locked to zero at a single wavelength (in this case 1.55µm) while the slope can be freely tuned.
To illustrate the flexibility of the design, we have fabricated a range of fibers with different combinations of pitch and hole-size. All fibers are drawn in lengths of 500 m and exhibit a structural uniformity (pitch and hole-size) better than 1% along the fiber. In Fig. 3 are shown measured dispersion curves for a range of fibers drawn with similar d/Λ of ~0.5 and increasing pitch in the range 1.34 – 1.47 µm. The pitch adjustment allows choosing the dispersion level at a given wavelength or tuning the zero-dispersion wavelength.
Slope tuning can be obtained by changing the hole-size as illustrated in Fig. 4 where the measured dispersion of four different fabricated fibers is shown. The dispersion at 1580 nm has been fixed at approximately -1 ps/(km·nm) and the slope is tuned from -3·10-2 to +1·10-2 ps/(km·nm2) by choosing holes in the range 0.47 – 0.50 µm and a pitch of 1.48 – 1.51 µm. Fiber 3 has a slope of less than 1·10-3 ps/(km·nm2), which is, to the best of our knowledge, more than one order of magnitude lower than the lowest slope ever reported for a nonlinear fiber. A broader dispersion curve of an equivalent fiber is shown in Fig. 5. The dispersion variation is within 1 ps/km/nm in the range 1465–1655 nm.
The attenuation of the fibers is in the range 12.5 to 7.9 dB/km at 1.55 µm and there is no sign of confinement or bending loss at this wavelength.
The nonlinear coefficient of the flat-slope fiber is approximately 11.2 (W·km)-1 measured by analyzing the self-phase modulation induced nonlinear phase shift from a dual frequency continuous wave source . The slope is tuned by adjusting the structural parameters and consequently, the effective area is changed in the process and the nonlinear coefficient therefore scales with the slope. In Fig. 6 are plotted the dispersion slope and the nonlinear coefficient as function of the relative hole size. The dispersion slope and the effective area are calculated and the nonlinear coefficient is then extracted from the effective area and the measurements on the flat slope fiber utilizing the fact that the effective area and the nonlinear coefficient are inversely proportional. The nonlinear coefficient scales linearly with the hole-size going from 9 (W·km)-1 at a hole-size of 0.44, to 13.5 (W·km)-1 at 0.56. The slope scales from +0.05 to -0.04 ps/(km·nm2) in the same relative hole-size range. Zero slope is obtained at a relative hole-size of 0.5. The behavior is independent of doping levels but the absolute values of the nonlinear coefficient and dispersion slope change with index difference between down- and up-doped regions. Higher index difference leads to higher nonlinear coefficient. The limit for the nonlinear coefficient is ultimately set by the achievable doping levels and the amount of loss tolerable as high germanium concentrations in the core increases the loss.
As the structure of the fiber features three-fold symmetry, there is no inherent birefringence to the design . In practice, however, the fibers exhibit a birefringence on the order of 10-5 – 10-4 (measured using a crossed polarizer technique ). The birefringence is believed to arise from asymmetry in the doped regions and stress, induced by the difference in thermal expansion coefficients and viscosity of the core elements.
We have demonstrated a novel type of nonlinear photonic crystal fiber with a triangular hybrid core region. By tuning the hole-size and pitch we have demonstrated how the dispersion of the fiber can be designed and fibers with negative, positive as well as near zero dispersion slope have been fabricated. The lowest slope obtained is 1·10-3 ps/(km·nm2) which is one order of magnitude lower than conventional slope reduced nonlinear fibers. This ultra low slope fiber has a nonlinear coefficient of 11.2 (W·km)-1. The fibers exhibit a loss down to 7.9 dB/km at 1.55 µm and can be spliced to standard single-mode step-index fibers with a loss of only 0.25 dB. The structural uniformity in the length direction is better than 1 % over 500m.
The author thanks Shin-Etsu Chemical Co., Ltd. Japan for providing the doped glass used in the fiber, Christophe Peucheret, COM, Technical University of Denmark for assistance in measurements of the nonlinear coefficient of the fibers and Jacob Riis Folkenberg for many fruitful technical discussions. This work was partly funded by the Danish Academy of Technical Sciences, ATV.
References and links
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