**4. Omniguiding fibers**

Omniguiding fibers generally assume structures having the core surrounded by dielectric cylindrical Bragg mirrors comprised of alternating layers of high and low refractive index values, thereby forming a 1D PBG configuration, as shown in **Figure 2**. These are also called as Bragg fibers. However, several forms of omniguiding fibers have been reported in the literature. In certain kinds, the core section may be solid dielectric (e.g., silica or Ge-doped silica). In the case of hollow-core Bragg fibers, the core may be filled up with air or any other gaseous medium, as shown in **Figure 3**. In these guides, light waves remain confined to the core region due to Bragg reflections from the dielectric mirrors. This is because the mirrors reflect a narrow range of wavelength within the angular range. As such, complete photonic band-gap regime exists in phase space above the light cone of the surrounding mediums [19].

The design of omniguiding Bragg fibers requires adjustments of parametric values, such as the core thickness and refractive index of the alternating highand low-index surrounding layered mediums. The number of layers also plays important roles in determining the allowed and forbidden wavelengths, i.e., the band-gap conditions. Omniguiding fibers may be designed as single-mode structure with no polarization degeneracy and without azimuthal dependence. The core size and number of concentric layers in these fibers govern the guided wavelengths, optical loss, and the effective single-mode operation [20]. As such,

*Cross-sectional view of a typical omniguiding Bragg fiber comprised of periodic multi-layered dielectric mirrors.*

**Figure 3.** *Cross-sectional view of a hollow-core omniguiding fiber.*

these may replace polarization maintaining fibers (PMFs)—the components that are used to eliminate the undesirable polarization dependent effects, such as polarization mode dispersion [21].

### **5. PhCs with defect**

In the periodic configuration of PhC, certain defect units may be deliberately introduced that destroy the periodicity of medium. For example, if in the 1D PhC structure of **Figure 1a**, a defect layer (or unit, in general) is introduced, the configuration would assume the form, as shown in **Figure 4**. In such a case, the transmission characteristics of spectra will be drastically altered. In such situations, defect modes emerge inside the PBG, resulting into the presence of very narrow peaks with large transmissivity. As such, the transmission spectra of PhCs with defect can be controlled, provided the *introduced* defect is comprised of functional materials so that the electromagnetic behavior of these may be externally controlled.

**5**

*Introductory Chapter: Photonic Crystals–Revisited DOI: http://dx.doi.org/10.5772/intechopen.85246*

**Figure 4.**

*Periodic medium with a defect unit.*

In general, the defect layer may be comprised of dielectric mediums or the mixture of dielectric and other kinds of mediums to yield a complex defect unit. In such situations, the transmission characteristics may be tailored in highly sophisticated ways, as described in ref. [22]. Apart from the planar structures, PCFs in certain forms may also have PhC cladding, wherein a central low-index structural defect

Various attempts have been made to analyze the modes in omniguiding Bragg fibers. The most common approach remains as the use of transfer matrix theory that can be applied to any cylindrically symmetric fiber structure surrounded with periodically stacked Bragg cladding [23]. In this kind of formalism, the exact treatment of arbitrary number of inner dielectric layers is taken into account, and the structure of the outermost clad is approximated in the asymptotic limit. The exploitation of transfer matrix theory can yield the confined modes in Bragg fibers by minimizing the radiation loss in the radial direction. Apart from this technique, the asymptotic analysis and finite difference time domain (FDTD) method may also be used [3]. The method of asymptotic analysis of omniguiding fibers involves dividing the bulk of periodic multi-layered cylindrical dielectric mirrors into two groups, namely the inner and outer ones. The former one is in close proximity of the core section, whereas the latter group is assumed to be at relatively larger distance from the center of fiber. In the analyses, however, both the kinds of groups involve several dielectric mirrors. Further, the field in the inner group is represented by Bessel functions, whereas that in the outer group is treated asymptotically using the plane wave approximation. It has been found that the results obtained in this formalism match very well with those achieved by implementing the FDTD technique and/or the transfer matrix method [5]. In the analyses of omniguiding Bragg fibers, the propagation of Bloch waves is of extreme importance to determine the nature of propagation. Within the context, Bloch wave constant remains vital to evaluate as a complex value of it shows the forbidden bands of the periodic structure, whereas a real-valued Bloch constant indicates the propagation of waves. In the former case, however, the fields are evanescent. Bragg fibers support modes that lie above the light line. These modes have the wave vector that corresponds to a frequency situated at the band-gap of multilayered dielectric mirror. The imaginary part of wave vector indicates the radiative loss of modes that decreases exponentially with the increasing number of layers. As stated before, the light wave propagation in Bragg fibers can be investigated in the analogy of electron flow in periodic lattice structures. This can be utilized in order to determine the working principle of omniguiding optical fibers. As such, the allowed and forbidden regions of these guides may be obtained by exploiting the quantum theory of electrons in solids. This has been justified that the use of simple Bloch formulation in omniguiding fibers exhibits continuous electric fields and power

would also be able to sustain the propagation of light waves.

**6. Analytical approach for omniguiding fibers**

*Introductory Chapter: Photonic Crystals–Revisited DOI: http://dx.doi.org/10.5772/intechopen.85246*

**Figure 4.** *Periodic medium with a defect unit.*

*Photonic Crystals - A Glimpse of the Current Research Trends*

these may replace polarization maintaining fibers (PMFs)—the components that are used to eliminate the undesirable polarization dependent effects, such as

*Cross-sectional view of a typical omniguiding Bragg fiber comprised of periodic multi-layered dielectric mirrors.*

In the periodic configuration of PhC, certain defect units may be deliberately introduced that destroy the periodicity of medium. For example, if in the 1D PhC structure of **Figure 1a**, a defect layer (or unit, in general) is introduced, the configuration would assume the form, as shown in **Figure 4**. In such a case, the transmission characteristics of spectra will be drastically altered. In such situations, defect modes emerge inside the PBG, resulting into the presence of very narrow peaks with large transmissivity. As such, the transmission spectra of PhCs with defect can be controlled, provided the *introduced* defect is comprised of functional materials so

that the electromagnetic behavior of these may be externally controlled.

polarization mode dispersion [21].

*Cross-sectional view of a hollow-core omniguiding fiber.*

**5. PhCs with defect**

**Figure 2.**

**Figure 3.**

**4**

In general, the defect layer may be comprised of dielectric mediums or the mixture of dielectric and other kinds of mediums to yield a complex defect unit. In such situations, the transmission characteristics may be tailored in highly sophisticated ways, as described in ref. [22]. Apart from the planar structures, PCFs in certain forms may also have PhC cladding, wherein a central low-index structural defect would also be able to sustain the propagation of light waves.
