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The propagation and dispersion properties of hollow-core Bragg fibre waveguides for both high and low refractive index contrasts of cladding materials are explored and compared in this chapter using two design wavelengths: 1550 nm in the near-infrared area and 632.8nm in the visible range. The boundary matching approach was used to build a relationship between the incoming and outgoing light waves employing the transfer matrix method. The observed photonic band gaps are somewhat substantial in high refractive index contrast cladding Bragg fibre waveguides, i.e. HRBFW, and low periodic cladding layers are required to achieve a perfect photonic bandgap. The spectrum range and spectral location of photonic band gaps in both HRBFW and low refractive index contrast cladding Bragg fibre waveguides, i.e. LRBFW, are substantially dependent on the angle of incidence of a light beam, i.e. the optical path of the incident light. The sensitivity of the Bragg fibre waveguide for sensing applications may be determined by measuring the thickness of the photonic bandgap or the spectral shift of the photonic bandgap. HRBFW seems to have a high sensitivity when considering the change in spectral bandwidth of photonic bandgap with core refractive index, which grows with increasing design wavelength. LRBFW has a much higher sensitivity than HRBFW when considering the LBE (Left band edge) and RBE (Right band edge), hence it is suggested for sensing applications. HRBFW directed a greater number of modes than LRBFW, according to the assessment of dispersion characteristics.

The adulteration of liquid fuels has several far-reaching repercussions, including pollution and a rising energy crisis. Around the world, fossil fuels are widely utilized for transportation and energy generation. Fuel adulteration currently threatens a big number of customers. Adulteration of fossil fuels with other recognised hydrocarbons is a common occurrence. Adulterants are added to these base fuels in the form of additional low-cost hydrocarbons with similar compositions, leading the base to be altered and degraded. Adulteration is an unauthorised or illegal introduction of a lower-quality external substance into a higher-quality commodity, causing the latter to lose its original composition and qualities. The Opto-Microfluidics approach is a new field that uses a small sample to identify adulteration in food and fuel, resulting in high-resolution findings. Consumers will benefit from very sensitive detection of dangerous adulteration in any commodity thanks to opto-microfluidic lab-on-chip technologies. Using the metal-polymer nanocomposites’ multilayer cylindrical nanostructure with a microfluidic channel, we develop a real-time and temperature dependent prototype of the Bragg Opto-microfluidic sensor for effective tracking of contaminated fossil fuels. The purpose of this chapter is to examine the biological motivations for the development of multilayer photonic nanostructures and various types of fuel adulteration detection optical sensors using various sensor-based techniques, as well as to compare the Bragg Metal-Polymer nanocomposites optical sensor with other optical sensors. This chapter is devoted entirely to the use of the theoretical model's Kay, Eykman, Dale-Gladstone, Newton, and Lorentz-Lorenz, as well as Hankel formalism and the transfer matrix method for cylindrical symmetry.

The performance study of various sensing parameters such as sensitivity, detection accuracy and quality parameter of liquid core Bragg fibre waveguide biosensor based on defect mode has been theoretically studied and compared with experimental findings of a similar structure without defect mode. The electromagnetic wave propagation in the present structure has been modelled using the transfer matrix method and Henkel formalism in cylindrical coordinates. The present multilayer structure can provide a band gap between 617 and 929 nm wavelength range at angle of incidence $$\theta = 70^{\circ }$$ . Due to the presence of a defect layer, a defect mode at 690 nm wavelength is observed in this band-gap region. This defect mode can be treated as a sensing signal in the present study. It is observed that the obtained sensitivity ( $$S\approx 334$$ nm/RIU) through the defect mode is almost the same as the experimental findings ( $$S\approx 330$$ nm/RIU) of a similar structure without the defect layer. But the obtained maximum detection accuracy (68.6) and quality parameter (160.4/RIU) of the present structure with defect layer is much larger than the values in a similar structure without defect layer (6.9 and 15/RIU). The present structure having a liquid-filled core, is therefore, favoured and useful in promising biosensing applications.

Theoretical analysis of Bragg fiber waveguide based inline optical filter having a defect layer is presented. Defect layer is introduced in Bragg fiber waveguide by breaking its cladding layer periodicity. Considering the cylindrical wave equations, the transmittance of proposed waveguide is obtained using transfer matrix method. It is observed that the proposed Bragg waveguide represent photonic band gap and a narrow defect mode (pass band) is present in this band gap region. This defect mode can be obtained in any position between the wavelength ranges 1.241 μm–1.550 μm with the help of incident angle of light. The narrowness of the defect mode depends on the number of unit cell present in the cladding region. This proposed waveguide may be used to design a narrowband transmission filters.

Performance parameter of a Bragg fiber waveguide based resonant sensor in presence of a defect layer in cladding regions is theoretically studied. The Bragg fiber waveguide consists of a liquid-core surrounded by alternate high and low refractive indices materials in cladding regions. Reflectivity of the proposed waveguide based resonant sensor is formulated using transfer matrix method for a non-homogeneous multilayer cylindrical system. The waveguide shows a band gap region with a narrow defect mode in the band gap region under the considered wavelength range. Instead of taking a whole band gap as a sensing signal, here the defect peak is taken as the sensing signal. It is observed that the intensity of defect mode is more sensitive for core refractive index than the intensity of traditional band gap region (lobe). This study shows that the higher sensitivity can be achieved by creating the defect at a position in cladding region where the intensity of transmitted light lies between 40% and 90%. Presence of a defect layer is able to increase the detection accuracy of the sensor and, hence increase the overall performance of this sensor.

In present communication, doubly tuned Bragg fiber waveguide low power inline optical filter with voltage tunable single crystal PMMA defect cavity is theoretically modeled and discussed using Henkel formalism in a cylindrical coordinate system for multiwavelength LASER applications. The structure provides photonic band gap (PBG) with a resonant transmission peak in the obtained PBG region. The defect cavity thickness is controlled by applying an external electric DC voltage. Initially, PBG of the proposed inline optical filter may tune-up to 828nm by modulating the incidence angle upto 80°. Thus, the resonant transmission peak also blue-shifted by 243nm, which can further tuned in presence of DC voltages and so-called doubly electrically tuned. Further, in doubly electrically tuned mode, the application range of such a device is very large up to 129nm for a small change in voltage range about 20V. Thus, the present device can be utilized as multiwavelength laser sources.

Sensing parameters of Bragg fiber waveguides having a defect layer in the cladding region are studied theoretically for bio-sensing and thickness monitoring applications. A comparison between Bragg fiber waveguides consist of a liquid-core surrounded with alternate high refractive index (R.I.) contrast of claddings and low R.I. contrast of claddings is presented. In non-homogeneous multilayer cylindrical system, the transmittance of proposed waveguide-based sensors is formulated using transfer matrix method and Hankel formalism. Both considered structures show photonic bandgap with a narrow passband in the bandgap region. This narrow passband is treated as sensing signal because its position and intensity depends on the diameter and refractive index of core material. The high refractive index contrast cladding waveguide shows larger intensity shift than low refractive index contrast cladding waveguide. The presence of defect layer in both considered waveguides is able to increase the sensing parameters like detection accuracy and overall performance.

A novel hollow core Bragg fiber waveguides having a defect layer are proposed and analyzed theoretically for sensing application. Matching the electric and magnetic fields at various interfaces, a relation between fields of first layer with final layer has been stabilized; hence, the equations for reflectance and transmittance of proposed structure are derived. Due to periodicity of concentric cylindrical structure, a perfect photonic band gap is observed in considered wavelength range. The presence of defect layer in cylindrical periodic structure shows a peak corresponding to defect mode in perfect photonic band gap region. The full width at half maxima of this peak depends on the periodicity of the cladding layers. Also, the spectral position and shift of peak of defect mode depend on the angle of incidence of light, refractive index of core material and design wavelength of structure. Therefore, it is more appropriate to consider this peak of defect mode as sensing signal instead of considering whole photonic band gap as sensing signal.

In present paper, an inline optical demultiplexer through cylindrical multilayered structure having a cavity of Poly-methyl methacrylate surrounded with single crystal 0.67PMN–0.33PT is presented. The required transmission of the proposed structure is obtained by transfer matrix method using cylindrical coordinate system. It is observed that the multilayer cylindrical structure is able to provide the photonic band gap, where groups of wavelengths are stopped from propagation through the waveguide. The insertion of cavity in considered structure also provides a pass band in the photonic band gap region. The 0.67PMN–0.33PT crystal in the present structure is used to control the thickness of cavity by applying an external DC voltage. Hence, the obtained shift of pass band is approximately 6 nm/V in the proposed structure.

Cylindrical Bragg waveguide based temperature sensor having a defect layer in cladding region is proposed and studied theoretically. The waveguide consists of SiC core surrounded by alternate Si and SiO 2 cladding layers with a defect layer. The transmittance of waveguide is obtained using transfer matrix method. It is observed that thermal expansion coefficient and refractive index of SiC varies linearly with temperature. The obtained sensitivity in our proposed sensor is approximately 51.48pm/Celsius, which is much larger than the reported 9pm/Celsius similar fiber Bragg grating based sensors.