**6. Conclusions**

38 Optical Communication

MHOF as given in Figure 9

**Figure 9.** Chromatic and waveguide dispersions for the MHOF with the five layers of air holes, the

**Figure 10.** Effective area for the fundamental mode versus the radius of the central air hole for the same

parameter values of = 2.0 μm and d = 1.2 μm, and different central core air holes

For the investigation of optical guidance properties of MHOFs, two numerical techniques of the FDTD and FDM are employed, considering extension to the analysis of holey optical fibers with random hole distributions in terms of material, shape, size, or location [11]. In this investigation, it is found that the outer radius (r) of the MHOF with = 2.0 μm, d = 1.2 μm, and the three hexagonal air-hole cladding layers doesn't affect the propagation characteristics significantly, if its thickness is about 6 times larger than the operating wavelength. And the 3-layer MHOF supports only a single mode over the wavelength range from 0.9 μm to 1.8 μm, whereas the MHOF with = 1.7 μm, d = 1.4 μm, and the single hexagonal air-hole cladding layer multimode guiding.

In the case of the MHOF with = 2.0 μm, d = 1.2 μm, and r = 12.0 μm, the guidance characteristics, such as normalized propagation constant, chromatic dispersion, mode field distribution, and effective area tend to change very little when the number of hexagonal airhole cladding layers becomes larger than five. In other words, adding more hexagonal airhole layers to the cladding beyond a certain point will not significantly affect the propagation constant, dispersion, and, in fact, all guidance properties of the MHOF waveguide.

By comparison, the size of the central core air hole has fair effect on the optical guidance properties of MHOFs. The MHOF with = 2.0 μm, d = 1.2 μm, b = 0.25 μm, and the five hexagonal cladding layers provides -4.2647 ps/nmkm of chromatic dispersion and 7.145 μm2 of effective area at = 1.55 μm. Similarly, the MHOF with the square air core of the equal area shows close results with -15.4055 ps/nmkm of the former and 6.7926 μm2 of the latter. As a general guideline, 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. Conversely, when the operating wavelength is longer, fields spread more to the cladding region and the index profile of the cladding region has more influence on these.

Even thought the holey optical fibers have complicated geometries, which make the electromagnetic analysis difficult, the results in this investigation can be utilized as a general guide. And depending on the desired applications, the MHOF with various design parameters are expected to be useful for novel developments related to optical communication in many areas.
