**1. Introduction**

Mirrors are important optical devices as these are greatly useful in applications, such as imaging, solar energy collection, and filtering. Also, these are indispensable in lasers in which the cavities constitute one of the components of prominence. Metallic and dielectric are the two common types of mirrors highly used in optics. Metallic mirrors reflect electromagnetic waves over a broad range of frequencies. But, these are not suitable for operations in the infrared (IR) and optical frequency regimes due to high absorption of optical power, thereby causing loss. As such, the bandwidth of operation of metallic mirrors (or guides) remains limited. However, dielectric medium-coated metallic guides can be used in the IR regime. Nevertheless, these have been proved to be inefficient for operations in the optical regime owing to the absorption loss in metals. As such, the use of conventional dielectric waveguides remains a preferred option for the transmission of optical frequencies.

Within the context of confinement of light waves in a cavity, the invention of photonic crystals (PhCs) opens up many possibilities of controlling the propagation of light. This made PhCs as the objects of intensive theoretical and experimental research. Properties of optical fibers having high-index core region surrounded by silica or air fall into the class of PhC; various forms of these have been vastly discussed in the literature [1]. It is interesting to note that PhCs having high-index cores possess many features of conventional optical fibers. However, PhCs exhibit photonic band-gap (PBG) effect, which relates to the forbidden regions in dispersion characteristics and transmission spectra—the feature that is distinct from the properties of high-index core optical fibers.

As PhCs have been a research topic in the frontline for quite some time, emphasizing the avenues of such specialized microstructures, the present chapter aims at throwing a glimpse of a few different forms of guides falling in the class of PhCs. Some of the novel applications of PhC-based structures and the current research trends in this specialized area are also touched upon.

### **2. Periodic band-gap structures**

PhCs can be classified to be one-, two-, or three-dimensional (1D, 2D, and 3D) periodic structures (depending on the kinds of periodic variation), comprised of materials with different refractive indices and having the periods comparable with the wavelengths of operation [2, 3]. Based on the configurations, there would be varieties of structures that can be regarded to be in the class of PhCs. For example, materials having periodic structures can exhibit the effect of PBG, provided the periodicity

**Figure 1.** *Periodic stratified mediums with (a) two-layer and (b) three-layer periodicity.*

remains on the scale of operating wavelength. Though the concept of periodic layered media had been put forward nearly over 40 years back [4, 5], varieties of new investigations in this front add many promising applications of such mediums. Mathematical formulations of symmetric periodic planar stratified mediums (**Figure 1a** and **b**) have been reported by the investigators [4]. The study deals with the evolution of explicit dispersion relations to determine the guided modes. In **Figure 1**, the periodicities in structure are of the forms of two (**Figure 1a**) and three layers (**Figure 1b**), respectively, which represent the variations in refractive index profiles. Apart from symmetric structures, the asymmetric dielectric film on a substrate is also quite a useful model among the more general types of optical waveguides.

The effects of PBG may be realized by the appropriate choice of periodic configurations, which involves dimensional features as well as the properties of constituent materials. This would result in forbidding the propagation of electromagnetic waves (through the structure) in certain frequency bands. It must be mentioned at this point that, recalling the Kronig-Penney model, the propagation of light waves in stratified periodic mediums can be compared with the situation of the movement of electrons in a periodic potential well [6, 7]. As such, if electrons can be diffracted by a periodic potential well, as evidenced by the theories of solid state physics, photons could equally be well-diffracted by a periodic modulation of the refractive index of medium. That is, such PBG mediums can be analyzed by exploiting the quantum theory of electrons in solids. This is because the basis for the guidance of light waves in dielectric mediums has a close analogy with the propagation of electrons in solid crystals—the fact that caused tremendous interests in PhCs and related research leading to the development of wide range of photonic structures for many novel applications [8]. In fact, multi-layered structures can reflect electromagnetic waves, if the frequency of operation lies within the gap. As such, stratified periodic structures have been proved to be prudent in exhibiting the property of spectral filtering.

## **3. Band-gap fibers**

A PhC fiber (PCF) is a class of 2D periodic structure, wherein the periodic variation occurs in the plane perpendicular to the fiber axis and an invariant structure along it. In PCFs, the core section has the refractive index above the effective index of the surrounding medium. The guidance of light waves happens due to the total

**3**

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

achieve fiber lasers having varieties of features [15].

and propagation loss.

**4. Omniguiding fibers**

internal reflection (TIR). PCFs exhibit band-gap characteristics and present promising optical properties, such as lower and flat dispersion over a very large range of wavelength and reduced optical nonlinearities. Apart from these, PCFs demonstrate

In certain PhC configurations, the clad region may be a matrix of different materials with high and low refractive index values, thereby forming a new hybrid material that greatly enhances the core-clad index difference [12]. Within the context, index-guiding and hollow-core are the two different kinds of PCF; the former one consists of a doped-solid dielectric or pure silica core placed inside an air-clad guide, whereas the latter kind confines light waves through the PBG effect. The use of PBG kind of PCF greatly helps in reducing optical nonlinearity

Among the others, PCFs are highly advantageous in fiber-based device applications. The invention of fiber-based lasers remains of special mention in this context. For example, continuous-wave fiber Brillouin lasers have been reported before utilizing highly nonlinear PCFs [13], wherein simple Fabry-Perot resonator plays the role of cavity. Apart from this, multi-wavelength Brillouin-erbium fiber lasers based on exploiting PCF with a linear cavity Fabry-Perot design have also been reported in the literature [14]. Many different schemes have been implemented to

Tunability of lasing systems using PCFs may be achieved in different ways. For example, one may use stimulated Brillouin scattering in the configurations [16, 17]. Within the context, the use of liquid crystals would also be greatly advantageous as these mediums exhibit the property of birefringence. Being liquid crystals as functional materials, one may recall the physical and/or chemical properties of liquid crystal, which can be altered by externally applied fields [18]. Apart from this, liquid crystals get affected due to the variations in temperature as well. As such, the thermal and electrical tuning of liquid crystals would alter the spectral characteristics—the feature that may be exploited in fabricating tunable PCFs. In fact, PCFs may be infiltrated with liquid crystals, in order to achieve tunable band-gap features.

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,

transparency in the far IR regime of electromagnetic spectrum [9–11].

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

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

among the more general types of optical waveguides.

*Periodic stratified mediums with (a) two-layer and (b) three-layer periodicity.*

remains on the scale of operating wavelength. Though the concept of periodic layered media had been put forward nearly over 40 years back [4, 5], varieties of new investigations in this front add many promising applications of such mediums. Mathematical formulations of symmetric periodic planar stratified mediums (**Figure 1a** and **b**) have been reported by the investigators [4]. The study deals with the evolution of explicit dispersion relations to determine the guided modes. In **Figure 1**, the periodicities in structure are of the forms of two (**Figure 1a**) and three layers (**Figure 1b**), respectively, which represent the variations in refractive index profiles. Apart from symmetric structures, the asymmetric dielectric film on a substrate is also quite a useful model

The effects of PBG may be realized by the appropriate choice of periodic configurations, which involves dimensional features as well as the properties of constituent materials. This would result in forbidding the propagation of electromagnetic waves (through the structure) in certain frequency bands. It must be mentioned at this point that, recalling the Kronig-Penney model, the propagation of light waves in stratified periodic mediums can be compared with the situation of the movement of electrons in a periodic potential well [6, 7]. As such, if electrons can be diffracted by a periodic potential well, as evidenced by the theories of solid state physics, photons could equally be well-diffracted by a periodic modulation of the refractive index of medium. That is, such PBG mediums can be analyzed by exploiting the quantum theory of electrons in solids. This is because the basis for the guidance of light waves in dielectric mediums has a close analogy with the propagation of electrons in solid crystals—the fact that caused tremendous interests in PhCs and related research leading to the development of wide range of photonic structures for many novel applications [8]. In fact, multi-layered structures can reflect electromagnetic waves, if the frequency of operation lies within the gap. As such, stratified periodic structures have been proved to be prudent in exhibiting the

A PhC fiber (PCF) is a class of 2D periodic structure, wherein the periodic variation occurs in the plane perpendicular to the fiber axis and an invariant structure along it. In PCFs, the core section has the refractive index above the effective index of the surrounding medium. The guidance of light waves happens due to the total

**2**

property of spectral filtering.

**3. Band-gap fibers**

**Figure 1.**

internal reflection (TIR). PCFs exhibit band-gap characteristics and present promising optical properties, such as lower and flat dispersion over a very large range of wavelength and reduced optical nonlinearities. Apart from these, PCFs demonstrate transparency in the far IR regime of electromagnetic spectrum [9–11].

In certain PhC configurations, the clad region may be a matrix of different materials with high and low refractive index values, thereby forming a new hybrid material that greatly enhances the core-clad index difference [12]. Within the context, index-guiding and hollow-core are the two different kinds of PCF; the former one consists of a doped-solid dielectric or pure silica core placed inside an air-clad guide, whereas the latter kind confines light waves through the PBG effect. The use of PBG kind of PCF greatly helps in reducing optical nonlinearity and propagation loss.

Among the others, PCFs are highly advantageous in fiber-based device applications. The invention of fiber-based lasers remains of special mention in this context. For example, continuous-wave fiber Brillouin lasers have been reported before utilizing highly nonlinear PCFs [13], wherein simple Fabry-Perot resonator plays the role of cavity. Apart from this, multi-wavelength Brillouin-erbium fiber lasers based on exploiting PCF with a linear cavity Fabry-Perot design have also been reported in the literature [14]. Many different schemes have been implemented to achieve fiber lasers having varieties of features [15].

Tunability of lasing systems using PCFs may be achieved in different ways. For example, one may use stimulated Brillouin scattering in the configurations [16, 17]. Within the context, the use of liquid crystals would also be greatly advantageous as these mediums exhibit the property of birefringence. Being liquid crystals as functional materials, one may recall the physical and/or chemical properties of liquid crystal, which can be altered by externally applied fields [18]. Apart from this, liquid crystals get affected due to the variations in temperature as well. As such, the thermal and electrical tuning of liquid crystals would alter the spectral characteristics—the feature that may be exploited in fabricating tunable PCFs. In fact, PCFs may be infiltrated with liquid crystals, in order to achieve tunable band-gap features.
