**5. Effects of the central air core on optical guidance properties**

36 Optical Communication

wavelength range.

wavelength for the fundamental mode in the MHOF with five hexagonal cladding layers of air holes. The cyan (light-blue) curve illustrates the waveguide dispersion for the same holey fiber without material dispersion included. Compared with the chromatic dispersion result, the waveguide dispersion varies rather gradually from about 78.985 ps/nmkm to 59.537 ps/nmkm over the wavelength range between 1.0 μm and 1.7 μm. It is noticed that the fivelayer MHOF provides positive chromatic and waveguide dispersions over the same

When the number of hexagonal air-hole cladding layers is changed from 5 to 3, it is noticed that the chromatic dispersion curves for the both cases are very close at the shorter wavelength range but deviation occurs from 1.2 μm. However, with the increased number of air-hole layers to 7, the Dch dispersion changes very close to the case of the five-layer MHOF. And adding more air-hole cladding layers like nine or eleven layers does not significantly change the chromatic dispersion result from the five-layer holey fiber in the operation wavelength of interest for general optical communications. This behaviour is reasonably attributed to the fact that when the operating wavelength is shorter, electromagnetic fields are more confined to the core region and only the core region has a major impact on the optical guidance properties. By comparison, when the operating wavelength is longer, fields spread more to the cladding region and the index profile of the

Incorporating the material dispersion for the MHOF with five layers of air holes, the field solution of the fundamental mode is obtained by using the finite difference technique. For instance, Figure 8 illustrates the normalized field pattern for the Ex electric component of the MHOF at the operating wavelength of 1.55 μm. Figure 8(a) demonstrates the top view with the colorbar scale in the right side and Figure 8(b) does the 3D view. As expected, it is observed that most of the energy is confined within the core region. Also for the fundamental mode of the MHOF with three, seven or nine cladding layers of air holes,

**Figure 8.** Normalized field pattern for the Ex electric component of the fundamental mode at = 1.55 μm in the MHOF with five layers of air holes and the parameter values of = 2.0 μm and d = 1.2 μm: (a)

cladding region has more influence on the effective refractive index.

about the same field shape is maintained at the same wavelength.

(a) (b)

top view with the colorbar scale; (b) 3D view

For the MHOF defined with the geometrical parameters of = 2.0 μm and d = 1.2 μm, and five cladding layers of air holes, how the core structure affects optical guidance properties is also investigated. By sizing the central air-hole radius (b) as shown in Figure 5, the MHOF with an air core is analyzed to obtain its propagation characteristics, based on FDM and FDTD methods for the full-vectorial analysis.

Getting the normalised propagation constant of the given optical fiber and computing its second derivative with respect to , dispersion characteristics can be evaluated. Figure 9 shows chromatic dispersion variations for the MHOF, as the radius of the central air hole is sized from 0 μm to 0.4 μm. This result indicates that the dispersion flatness can be achieved around 1.3-μm wavelength by designing the MHOF with b = 0.25 μm. Specifically, the chromatic dispersion (ps/nmkm) is -0.7724, 0.2635, -0.4532 at wavelengths of 1.2, 1.3, and 1.4 μm, respectively. This near-zero ultra-flattened dispersion is highly desirable in long-haul fiber-optic communication systems.

When the circular hole at the center is changed to the square air hole with the side length (s) of 0.4432 μm, which has the area equal to that of the former, the chromatic dispersion versus wavelength for the fundamental mode in the MHOF is also depicted as the green dashed line with the diamond symbols in Figure 9. As noticed, the chromatic dispersion curves for the both cases are close at the shorter wavelength range around 1.0 μm, compared to the gap between two curves at the wavelength range around 1.7 μm.

The effective area for the fundamental mode is also evaluated by using the field distribution results, as shown in Figure 10. The red dashed line represents the effective area for the MHOF at the operating wavelength of 1.3 μm and the blue solid line at 1.55 μm, as the radius of the core hole (b) is sized from 0 to 0.6 μm. It is noted that the effective core area tends to increase with the size of the central air hole at both the operation wavelengths. The reason is that with bigger core hole the electromagnetic fields spread further into the cladding region. Thus sizing the core hole provides a decent way to control the effective area. Also, notice that the effective areas at the longer wavelength of 1.55 μm generally result in larger values for each different hole radius, compared to those at 1.3 μm. While the effective area is 6.7926 μm2 for the MHOF with s = 0.4432 μm at = 1.55 μm, as indicated by the dotted line, those with b = 0.25 μm at = 1.3 μm and 1.55 μm are 6.691 μm2 and 7.145 μm2, respectively.

**Figure 9.** Chromatic and waveguide dispersions for the MHOF with the five layers of air holes, the parameter values of = 2.0 μm and d = 1.2 μm, and different central core air holes

**Figure 10.** Effective area for the fundamental mode versus the radius of the central air hole for the same MHOF as given in Figure 9
